# A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

## Abstract

#### Citation

Rach, R. (2012), "A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011", *Kybernetes*, Vol. 41 No. 7/8. https://doi.org/10.1108/k.2012.06741gaa.007

### Publisher

:Emerald Group Publishing Limited

Copyright © 2012, Emerald Group Publishing Limited

## A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

**Article Type:** Communications and forum **From:**
Kybernetes, Volume 41, Issue 7/8

**In memoriam Distinguished Professor and the David C. Barrow Professor of
Mathematics Dr George Adomian**

I am pleased to submit my comprehensive worldwide bibliography on the Adomian
decomposition method: “A bibliography of the theory and applications of
the Adomian decomposition method, 1961-2011”. It comprises over 900 titles
for research papers and books by a wide variety of authors and nationalities and
I consider it to be a constructive bibliography in that it features papers and
books that advance the technique and extend the application of the Adomian
decomposition method for solving nonlinear stochastic differential, integral,
integro-differential and operator equations that model man-made device
performance parameters and natural phenomena. As it has been 50 years since Dr
George Adomian began his innovative research in 1961, I thought it to be
appropriate to compile such a technical bibliography in memoriam. I also
recalled your readers’ interest in a bibliography of his research
publications after his death in 1996, and hence I thought of *Kybernetes*
in this regard for its wide circulation among cyberneticists, systems analysts,
mathematicians, scientists and engineers.

**Bibliography**

Abadyan, M., Beni, Y.T. and Noghrehabadi, A. (2011), “Investigation of
elastic boundary condition on the pull-in instability of beam-type NEMS under
van der Waals attraction”, *Procedia Engineering*, Vol. 10, pp.
1724-9.

Abassy, T.A. (2010), “Improved Adomian decomposition method”, *Computers
and Mathematics with Applications*, Vol. 59 No. 1, pp. 42-54.

Abbaoui, K. (1995), “Thèse de l’Université Pierre et
Marie Curie – Paris VI”, *Les fondements mathématiques de la
méthode décompositionnelle d’Adomian et application à la résolution
de problèmes issus de la biologie et de la médicine, Université
Pierre et Marie Curie – Paris VI, Paris, France, 4 October 1995*.

Abbaoui, K. (1997), “Thèse d’Etat – Université de
Sétif”, *La méthode décompositionnelle d’Adomian et
ses applications, Université de Sétif, Sétif, Algeria, 15
December 1997*.

Abbaoui, K. and Cherruault, Y. (1994a), “Convergence of Adomian’s
method applied to differential equations”, *Computers and Mathematics
with Applications*, Vol. 28 No. 5, pp. 103-9.

Abbaoui, K. and Cherruault, Y. (1994b), “Convergence of Adomian’s
method applied to nonlinear equations”, *Mathematical and Computer
Modelling*, Vol. 20 No. 9, pp. 60-73.

Abbaoui, K. and Cherruault, Y. (1994c), “New ideas for solving
identification and optimal control problems related to biomedical systems”,
*International Journal of Bio-Medical Computing*, Vol. 36 No. 3, pp.
181-6.

Abbaoui, K. and Cherruault, Y. (1995), “New ideas for proving
convergence of decomposition methods”, *Computers and Mathematics with
Applications*, Vol. 29 No. 7, pp. 103-8.

Abbaoui, K. and Cherruault, Y. (1999), “The decomposition method
applied to the Cauchy problem”, *Kybernetes*, Vol. 28 No. 1, pp.
68-74.

Abbaoui, K., Cherruault, Y. and N’Dour, M. (1995), “The
decomposition method applied to differential systems”, *Kybernetes*,
Vol. 24 No. 8, pp. 32-40.

Abbaoui, K., Cherruault, Y. and Seng, V. (1995), “Practical formulae
for the calculus of multivariable Adomian polynomials”, *Mathematical
and Computer Modelling*, Vol. 22 No. 1, pp. 89-93.

Abbaoui, K., Pujol, M.J., Cherruault, Y., Himoun, N. and Grimalt, P. (2001),
“A new formulation of Adomian method: convergence result”, *Kybernetes*,
Vol. 30 Nos 9/10, pp. 1183-91.

Abbasbandy, S. (2003), “Improving Newton-Raphson method for nonlinear
equations by modified Adomian decomposition method”, *Applied
Mathematics and Computation*, Vol. 145 Nos. 2/3, pp. 887-93.

Abbasbandy, S. (2005), “Extended Newton’s method for a system of
nonlinear equations by modified Adomian decomposition method”, *Applied
Mathematics and Computation*, Vol. 170 No. 1, pp. 648-56.

Abbasbandy, S. (2007), “A numerical solution of Blasius equation by
Adomian’s decomposition method and comparison with homotopy perturbation
method”, *Chaos, Solitons & Fractals*, Vol. 31 No. 1, pp.
257-60.

Abbasbandy, S. and Darvishi, M.T. (2005a), “A numerical solution of
Burgers’ equation by modified Adomian method”, *Applied Mathematics
and Computation*, Vol. 163 No. 3, pp. 1265-72.

Abbasbandy, S. and Darvishi, M.T. (2005b), “A numerical solution of
Burgers’ equation by time discretization of Adomian’s decomposition
method”, *Applied Mathematics and Computation*, Vol. 170 No. 1, pp.
95-102.

Abdelrazec, A. (2008), “Adomian decomposition method: convergence analysis and numerical approximations”, MSc thesis (Mathematics), McMaster University, Hamilton, Ontario, Canada, November 2008, available at: www.dmpeli.mcmaster.ca/PaperBank/ThesisAhmed.pdf

Abdelrazec, A. and Pelinovsky, D. (2011), “Convergence of the Adomian
decomposition method for initial-value problems”, *Numerical Methods for
Partial Differential Equations*, Vol. 27 No. 4, pp. 749-66.

Abdelwahid, F. (2003), “A mathematical model of Adomian polynomials”,
*Applied Mathematics and Computation*, Vol. 141 Nos 2/3, pp. 447-53.

Abdelwahid, F. and Rach, R. (2009), “On the foundation of the Adomian
decomposition method”, *Journal of Natural and Physical Sciences*,
Vol. 23 Nos 1/2, pp. 13-29.

Abdulaziz, O., Noor, N.F.M., Hashim, I. and Noorani, M.S.M. (2008), “Further
accuracy tests on Adomian decomposition method for chaotic systems”, *Chaos,
Solitons and Fractals*, Vol. 36 No. 5, pp. 1405-11.

Achouri, T. and Omrani, K. (2009), “Numerical solutions for the damped
generalized regularized long-wave equation with a variable coefficient by
Adomian decomposition method”, *Communications in Nonlinear Science and
Numerical Simulation*, Vol. 14 No. 5, pp. 2025-33.

Adesanya, S.O. and Ayeni, E.R.O. (2011), “Existence and uniqueness
result for couple stress bio-fluid flow model via Adomian decomposition method”,
*International Journal of Nonlinear Science*, Vol. 12 No. 1, pp. 16-24,
available at: www.internonlinearscience.org/upload/papers/20110915065005565.pdf

Adjedj, B. (1999), “Application of the decomposition method to the
understanding of HIV immune dynamics”, *Kybernetes*, Vol. 28 No. 3,
pp. 271-83.

Adomian, G., Howard Hughes Fellow, (1961), “Linear stochastic operators”, PhD dissertation (Physics), University of California at Los Angeles, Los Angeles, CA, August 1961 and July 1963; Microfilm Accession No. AAT 6402269, ProQuest/UMI (University Microfilms, Inc.), Ann Arbor, MI, February 1964.

Adomian, G. (1963a), “Linear randomly-varying systems”, in Nomura,
T. (Ed.), *Proceedings of the Fourth International Symposium on Space
Technology and Science, Tokyo, Japan, 1962*, Japan Publications Trading Co.,
Tokyo, p. 634.

Adomian, G. (1963b), “Linear stochastic operators”, *Reviews of
Modern Physics*, Vol. 35 No. 1, pp. 185-207.

Adomian, G. (1964), “Stochastic Green’s functions”, in
Bellman, R.E. (Ed.), *Proceedings of Symposia in Applied Mathematics, Vol.
XVI: Stochastic Processes in Mathematical Physics and Engineering; Proceedings
of a Symposium in Applied Mathematics of the American Mathematical Society, New
York, NY, USA, April 30-May 2, 1963*, American Mathematical Society,
Providence, RI, pp. 1-39.

Adomian, G. (1967), “Theory of random systems”, in Kožešnik,
J. (Ed.), *Transactions of the Fourth Prague Conference on Information
Theory, Statistical Decision Functions, Random Processes, Prague,
Czechoslovakia, August 31-September 11, 1965*, Academia, Prague and Academic
Press, New York, NY, pp. 205-22.

Adomian, G. (1970), “Random operator equations in mathematical physics.
I”, *Journal of Mathematical Physics*, Vol. 11 No. 3, pp. 1069-84.

Adomian, G. (1971a), “Linear random operator equations in mathematical
physics. II”, *Journal of Mathematical Physics*, Vol. 12 No. 9, pp.
1944-8.

Adomian, G. (1971b), “Linear random operator equations in mathematical
physics. III”, *Journal of Mathematical Physics*, Vol. 12 No. 9, pp.
1948-55.

Adomian, G. (1971c), “Erratum: random operator equations in
mathematical physics. I, (*J. Math. Phys.* Vol. 11, 1069 (1970))”,
*Journal of Mathematical Physics*, Vol. 12 No. 7, p. 1446.

Adomian, G. (1971d), “Erratum: random operator equations in
mathematical physics. I, (*J. Math. Phys.* Vol. 11, 1069 (1970))”,
*Journal of Mathematical Physics*, Vol. 12 No. 9, p. 2031.

Adomian, G. (1971e), “The closure approximation in the hierarchy
equations”, *Journal of Statistical Physics*, Vol. 3 No. 2, pp.
127-33.

Adomian, G. (1972), “Addendum: linear random operator equations in
mathematical physics. III, (*J. Math. Phys.* Vol. 12, 1948 (1971))”,
*Journal of Mathematical Physics*, Vol. 13 No. 2, p. 272.

Adomian, G. (1975), “Obtaining first and second order statistics <*y*>
and *R*_{y}(*t*_{1},*t*_{2})
in stochastic differential equations for the nonlinear case”, , Vol. 10 No. 6, pp. 529-34.

Adomian, G. (1976), “Nonlinear stochastic differential equations”,
*Journal of Mathematical Analysis and Applications*, Vol. 55 No. 2, pp.
441-52.

Adomian, G. (1977), “The solution of general linear and nonlinear
stochastic systems”, in Rose, J. and Bilciu, C. (Eds.), *Modern Trends
in Cybernetics and Systems; in Three Volumes; Proceedings of the Third
International Congress of Cybernetics and Systems, Bucharest, Romania, August
25-29, 1975; Volume II*, Springer, Berlin, pp. 203-14.

Adomian, G. (1978a), “On the existence of solutions for linear and
nonlinear stochastic operator equations”, *Journal of Mathematical
Analysis and Applications*, Vol. 62 No. 2, pp. 229-35.

Adomian, G. (1978b), “New results in stochastic equations – the
nonlinear case”, in Lakshmikantham, V. (Ed.), *Nonlinear Equations in
Abstract Spaces; Proceedings of an International Symposium on Nonlinear
Equations in Abstract Spaces, University of Texas at Arlington, Arlington, TX,
USA, June 8-10, 1977*, Academic Press, New York, NY, pp. 3-23.

Adomian, G. (1979a), “A constructive method for linear and nonlinear
stochastic partial differential equations”, in Lakshmikantham, V. (Ed.),
*Applied Nonlinear Analysis;* *Proceedings of an International
Conference on Applied Nonlinear Analysis, University of Texas at Arlington,
Arlington, TX, USA, April 20-22, 1978*, Academic Press, New York, NY, pp.
13-23.

Adomian, G. (1979b), “Stochastic operators and dynamical systems”,
in Wang, P.C.C., Schoenstadt, A.L., Russak, B.I. and Comstock, C. (Eds.), *Information
Linkage between Applied Mathematics and Industry; Proceedings of the First
Annual Workshop on the Information Linkage between Applied Mathematics and
Industry, Naval Postgraduate School, Monterey, CA, USA, February 23-25, 1978*,
Academic Press, New York, NY, pp. 581-96.

Adomian, G. (1980), “Stochastic systems analysis”, in Adomian, G.
(Ed.), *Applied Stochastic Processes; Proceedings of the Applied Stochastic
Processes Conference, Center for Applied Mathematics, University of Georgia,
Athens, GA, USA, May 15-19, 1978*, Academic Press, New York, NY, pp. 1-17.

Adomian, G. (1981a), “On product nonlinearities in stochastic
differential equations”, *Applied Mathematics and Computation*, Vol.
8 No. 1, pp. 79-82.

Adomian, G. (1981b), “Stochastic nonlinear modeling of fluctuations in
a nuclear reactor – a new approach”, *Annals of Nuclear Energy*,
Vol. 8 No. 7, pp. 329-30.

Adomian, G. (1982a), “Stochastic model for colored noise”, *Journal
of Mathematical Analysis and Applications*, Vol. 88 No. 2, pp. 607-9.

Adomian, G. (1982b), “On Green’s function in higher order
stochastic differential equations”, *Journal of Mathematical Analysis
and Applications*, Vol. 88 No. 2, pp. 604-6.

Adomian, G. (1982c), “Solution of nonlinear stochastic physical
problems”, *Rendiconti del Seminario Matematico Università e
Politecnico di Torino*, Vol. 40, No. Special, pp. 7-22.

Adomian, G. (1982d), “Stabilization of a stochastic nonlinear economy”,
*Journal of Mathematical Analysis and Applications*, Vol. 88 No. 1, pp.
306-17.

Adomian, G. (1982e), “Application of stochastic differential equations to economics”, in Stochastic Differential Equations; Proceedings of the “5-Tage-Kurs” of the USP Mathematisierung at Bielefeld University, Bielefeld, Germany, October 12-16, 1981; Materialien des Universitätsschwerpunktes Mathematisierung der Einzelwissenschaften, Vol. 38, Universität Bielefeld, Bielefeld, Germany.

Adomian, G. (1983a), “Approximate calculation of Green’s functions”,
*Journal of Approximation Theory*, Vol. 37 No. 2, pp. 119-24.

Adomian, G. (1983b), “Partial differential equations with integral
boundary conditions”, *Computers and Mathematics with Applications*,
Vol. 9 No. 3, pp. 443-5.

Adomian, G. (1983c), *Stochastic Systems*, Academic Press, New York,
NY.

Adomian, G. (1984a), “A new approach to nonlinear partial differential
equations”, *Journal of Mathematical Analysis and Applications*,
Vol. 102 No. 2, pp. 420-34.

Adomian, G. (1984b), “Convergent series solution of nonlinear equations”,
*Journal of Computational and Applied Mathematics*, Vol. 11 No. 2, pp.
225-30.

Adomian, G. (1984c), “On the convergence region for decomposition
solutions”, *Journal of Computational and Applied Mathematics*, Vol.
11 No. 3, pp. 379-80.

Adomian, G. (1985a), “Discretization, decomposition and supercomputers”,
*Journal of Mathematical Analysis and Applications*, Vol. 112 No. 2, pp.
487-96.

Adomian, G. (1985b), “New approaches to solution of national economy
models and business cycles”, *Kybernetes*, Vol. 14 No. 4, pp. 221-3.

Adomian, G. (1985c), “Nonlinear stochastic dynamical systems in
physical problems”, *Journal of Mathematical Analysis and Applications*,
Vol. 111 No. 1, pp. 105-13.

Adomian, G. (1985d), “Random eigenvalue equations”, *Journal of
Mathematical Analysis and Applications*, Vol. 111 No. 2, pp. 427-32.

Adomian, G. (1986a), “A new approach to the heat equation – an
application of the decomposition method”, *Journal of Mathematical
Analysis and Applications*, Vol. 113 No. 1, pp. 202-9.

Adomian, G. (1986b), “Application of the decomposition method to the
Navier-Stokes equations”, *Journal of Mathematical Analysis and
Applications*, Vol. 119 Nos 1/2, pp. 340-60.

Adomian, G. (1986c), “Inversion of matrices”, *Mathematics and
Computers in Simulation*, Vol. 28 No. 2, pp. 151-3.

Adomian, G. (1986d), “Nonlinear equations with mixed derivatives”,
*Journal of Mathematical Analysis and Applications*, Vol. 120 No. 2, pp.
734-6.

Adomian, G. (1986e), “Nonlinear hyperbolic initial value problem”,
*Journal of Mathematical Analysis and Applications*, Vol. 120 No. 2, pp.
730-3.

Adomian, G. (1986f), “Solution of the Navier-Stokes equation – I”,
*Computers and Mathematics with Applications*, Vol. 12 No. 11, Pt. A, pp.
1119-24.

Adomian, G. (1986g), “Solution of Lanchester equation models for combat”,
*Journal of Mathematical Analysis and Applications*, Vol. 114 No. 1, pp.
176-7.

Adomian, G. (1986h), “Solution of algebraic equations”, *Mathematics
and Computers in Simulation*, Vol. 28 No. 2, pp. 155-7.

Adomian, G. (1986i), “Stochastic water reservoir modeling”, *Journal
of Mathematical Analysis and Applications*, Vol. 115 No. 1, pp. 233-4.

Adomian, G. (1986j), “Systems of nonlinear partial differential
equations”, *Journal of Mathematical Analysis and Applications*,
Vol. 115 No. 1, pp. 235-8.

Adomian, G. (1986k), “State-delayed matrix differential-difference
equations”, *Journal of Mathematical Analysis and Applications*,
Vol. 114 No. 2, pp. 426-8.

Adomian, G. (1986l), “The decomposition method for nonlinear dynamical
systems”, *Journal of Mathematical Analysis and Applications*, Vol.
120 No. 1, pp. 370-83.

Adomian, G. (1986m), “Decomposition solution for Duffing and van der
Pol oscillators”, *International Journal of Mathematics and Mathematical
Sciences*, Vol. 9 No. 4, pp. 731-2, doi:10.1155/S016117128600087X.

Adomian, G. (1986n), *Nonlinear Stochastic Operator Equations*,
Academic Press, Orlando, FL.

Adomian, G. (1987a), “Vibration in offshore structures: an analysis for
the general nonlinear stochastic case – Part I”, *Mathematics and
Computers in Simulation*, Vol. 29 No. 2, pp. 119-22.

Adomian, G. (1987b), “Vibration in offshore structures – Part II”,
*Mathematics and Computers in Simulation*, Vol. 29 No. 5, pp. 351-6.

Adomian, G. (1987c), “Wave propagation in nonlinear media”, *Applied
Mathematics and Computation*, Vol. 24 No. 4, pp. 311-32.

Adomian, G. (1987d), “Semilinear wave equations”, *Computers
and Mathematics with Applications*, Vol. 14 No. 6, pp. 497-9.

Adomian, G. (1987e), “Nonlinear oscillations in physical systems”,
*Mathematics and Computers in Simulation*, Vol. 29 Nos. 3/4, pp. 275-84.

Adomian, G. (1987f), “A general approach to solution of partial
differential equation systems”, *Computers and Mathematics with
Applications*, Vol. 13 Nos. 9/11, pp. 741-7.

Adomian, G. (1987g), “A new approach to the Efinger model for a
nonlinear quantum theory for gravitating particles”, *Foundations of
Physics*, Vol. 17 No. 4, pp. 419-23.

Adomian, G. (1987h), “An investigation of the asymptotic decomposition
method for nonlinear equations in physics”, *Applied Mathematics and
Computation*, Vol. 24 No. 1, pp. 1-17.

Adomian, G. (1987i), “Modeling and solving physical problems”, *Mathematical
Modelling*, Vol. 8, pp. 57-60.

Adomian, G. (1987j), “Modification of the decomposition approach to the
heat equation”, *Journal of Mathematical Analysis and Applications*,
Vol. 124 No. 1, pp. 290-1.

Adomian, G. (1987k), “Analytical solutions for ordinary and partial
differential equations”, in Knowles, I.W. and Saito, Y. (Eds.), *Differential
Equations and Mathematical Physics; Proceedings of an International Conference,
Birmingham, Alabama, USA, March 3-8, 1986*, Lecture Notes in Mathematics
(LNM), Vol. 1285, Springer, Berlin, pp. 1-15.

(1987l),

Adomian, G. (1988a), “A general approach for complex systems”, *Kybernetes*,
Vol. 17 No. 1, pp. 49-59.

Adomian, G. (1988b), “A new approach to Burger’s equation”,
*Physica D: Nonlinear Phenomena*, Vol. 31 No. 1, pp. 65-9.

Adomian, G. (1988c), “A review of the decomposition method in applied
mathematics”, *Journal of Mathematical Analysis and Applications*,
Vol. 135 No. 2, pp. 501-44.

Adomian, G. (1988d), “An adaptation of the decomposition method for
asymptotic solutions”, *Mathematics and Computers in Simulation*,
Vol. 30 No. 4, pp. 325-9.

Adomian, G. (1988e), “Analysis of model equations of gas dynamics”,
*AIAA Journal*, Vol. 26 No. 2, pp. 242-4.

Adomian, G. (1988f), “Analytic solutions for nonlinear equations”,
*Applied Mathematics and Computation*, Vol. 26 No. 1, pp. 77-88.

Adomian, G. (1988g), “Application of decomposition to
convection-diffusion equations”, *Applied Mathematics Letters*, Vol.
1 No. 1, pp. 7-9.

Adomian, G. (1988h), “Corrigenda and comment on ‘a general
approach to solution of partial differential equation systems’”, *Computers
and Mathematics with Applications*, Vol. 15 Nos. 6/8, p. 711.

Adomian, G. (1988i), “Elliptic equations and decomposition”, *Computers
and Mathematics with Applications*, Vol. 15 No. 1, pp. 65-7.

Adomian, G. (1988j), “New approach to the analysis and control of large
space structures”, *AIAA Journal*, Vol. 26 No. 3, pp. 377-80.

Adomian, G. (1988k), “Propagation in dissipative or dispersive media”,
*Journal of Computational and Applied Mathematics*, Vol. 23 No. 3, pp.
395-6.

Adomian, G. (1988l), “Solving the nonlinear equations of physics”,
*Computers and Mathematics with Applications*, Vol. 16 Nos 10/11, pp.
903-14.

Adomian, G. (1989a), “Application of decomposition to hyperbolic,
parabolic, and elliptic partial differential equations”, *International
Journal of Mathematics and Mathematical Sciences*, Vol. 12 No. 1, pp.
137-44.

Adomian, G. (1989b), “Comments on a ‘counterexample’ to
decomposition”, *Journal of Computational and Applied Mathematics*,
Vol. 26 No. 3, pp. 375-6.

Adomian, G. (1989c), “Speculations on possible directions and
applications for the decomposition method”, in Blaquiére, A. (Ed.),
*Modeling and Control of Systems in Engineering, Quantum Mechanics, Economics
and Biosciences; Proceedings of the Third Bellman Continuum Workshop, Sophia
Antipolis, France, June 13-14, 1988*, Lecture Notes in Control and
Information Sciences (LNCIS), Vol. 121, Springer, Berlin, pp. 479-95.

Adomian, G. (1989d), *Nonlinear Stochastic Systems Theory and Applications
to Physics*, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1990), “Decomposition solution of nonlinear hyperbolic
equations”, *Mathematical and Computer Modelling*, Vol. 14, pp.
80-2.

Adomian, G. (1991a), “A review of the decomposition method and some
recent results for nonlinear equations”, *Computers and Mathematics with
Applications*, Vol. 21 No. 5, pp. 101-27.

Adomian, G. (1991b), “An analytical solution of the stochastic
Navier-Stokes system”, *Foundations of Physics*, Vol. 21 No. 7, pp.
831-43.

Adomian, G. (1991c), “Solving frontier problems modelled by nonlinear
partial differential equations”, *Computers and Mathematics with
Applications*, Vol. 22 No. 8, pp. 91-4.

Adomian, G. (1991d), “The sine-Gordon, Klein-Gordon and Korteweg-de
Vries equations”, *Computers and Mathematics with Applications*,
Vol. 21 No. 5, pp. 133-6.

Adomian, G. (1991e), “Errata to ‘a review of the decomposition
method and some recent results for nonlinear equations’: (*Computers
Math. Applic.*, Vol. 21 No. 5, 1991, pp. 101*-*127)”, *Computers
and Mathematics with Applications*, Vol. 22 No. 8, p. 95.

Adomian, G. (1993a) “A class of nonlinear relativistic partial
differential equations in elementary particle theory”, *Foundations of
Physics Letters*, Vol. 6 No. 6, pp. 603-5.

Adomian, G. (1993b) “The N-body problem”, *Foundations of
Physics Letters*, Vol. 6 No. 6, pp. 597-602.

Adomian, G. (1994a) “Solution of nonlinear evolution equations”,
*Mathematical and Computer Modelling*, Vol. 20 No. 12, pp. 1-2.

Adomian, G. (1994b) “Solution of physical problems by decomposition”,
*Computers and Mathematics with Applications*, Vol. 27 Nos 9/10, pp.
145-54.

Adomian, G. (1994c) “The origin of chaos”, *Foundations of
Physics Letters*, Vol. 7 No. 6, pp. 585-9.

Adomian, G. (1994d), *Solving Frontier Problems of Physics: The
Decomposition Method*, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1995a), “Solving the mathematical models of neurosciences
and medicine”, *Mathematics and Computers in Simulation*, Vol. 40
Nos 1/2, pp. 107-14.

Adomian, G. (1995b), “A new approach to solution of the Maxwell
equations”, *Foundations of Physics Letters*, Vol. 8 No. 6, pp.
583-7.

Adomian, G. (1995c), “Analytical solution of Navier-Stokes flow of a
viscous compressible fluid”, *Foundations of Physics Letters*, Vol.
8 No. 4, pp. 389-400.

Adomian, G. (1995d), “Delayed nonlinear dynamical systems”, *Mathematical
and Computer Modelling*, Vol. 22 No. 3, pp. 77-9.

Adomian, G. (1995e), “Fisher-Kolmogorov equation”, *Applied
Mathematics Letters*, Vol. 8 No. 2, pp. 51-2.

Adomian, G. (1995f), “On integral, differential and
integro-differential equations, perturbation and averaging methods”, *Kybernetes*,
Vol. 24 No. 7, pp. 52-60.

Adomian, G. (1995g), “Random Volterra integral equations”, *Mathematical
and Computer Modelling*, Vol. 22 No. 8, pp. 101-2.

Adomian, G. (1995h), “Stochastic Burgers’ equation”, *Mathematical
and Computer Modelling*, Vol. 22 No. 8, pp. 103-5.

Adomian, G. (1995i), “The diffusion-Brusselator equation”, *Computers
and Mathematics with Applications*, Vol. 29 No. 5, pp. 1-3.

Adomian, G. (1995j), “The Nikolaevskiy model for nonlinear seismic
waves”, *Mathematical and Computer Modelling*, Vol. 22 No. 3, pp.
81-2.

Adomian, G. (1995k), “The generalized Kolmogorov-Petrovskii-Piskunov
equation”, *Foundations of Physics Letters*, Vol. 8 No. 1, pp.
99-101.

Adomian, G. (1996a), “The Kadomtsev-Petviashvili equation”, *Applied
Mathematics and Computation*, Vol. 76 No. 1, pp. 95-7.

Adomian, G. (1996b), “A non-perturbative solution of N-body dynamics”,
*Foundations of Physics Letters*, Vol. 9 No. 3, pp. 301-8.

Adomian, G. (1996c), “Coupled Maxwell equations for electromagnetic
scattering”, *Applied Mathematics and Computation*, Vol. 77 Nos 2/3,
pp. 133-5.

Adomian, G. (1996d), “Nonlinear Klein-Gordon equation”, *Applied
Mathematics Letters*, Vol. 9 No. 3, pp. 9-10.

Adomian, G. (1996e), “Nonlinear random vibration”, *Applied
Mathematics and Computation*, Vol. 77 Nos 2/3, pp. 109-12.

Adomian, G. (1996f), “Solution of coupled nonlinear partial
differential equations by decomposition”, *Computers and Mathematics
with Applications*, Vol. 31 No. 6, pp. 117-20.

Adomian, G. (1996g), “The Burridge-Knopoff model”, *Applied
Mathematics and Computation*, Vol. 77 Nos 2/3, pp. 131-2.

Adomian, G. (1996h), “The dissipative sine-Gordon equation”, *Foundations
of Physics Letters*, Vol. 9 No. 4, pp. 407-10.

Adomian, G. (1996i), “The fifth-order Korteweg-de Vries equation”,
*International Journal of Mathematics and Mathematical Sciences*, Vol. 19
No. 2, p. 415, doi:10.1155/S0161171296000592.

Adomian, G. (1997a), “Explicit solutions of nonlinear partial
differential equations”, *Applied Mathematics and Computation*, Vol.
88 Nos. 2/3, pp. 117-26.

Adomian, G. (1997b), “Non-perturbative solution of the
Klein-Gordon-Zakharov equation”, *Applied Mathematics and Computation*,
Vol. 81 No. 1, pp. 89-92.

Adomian, G. (1997c), “On KdV type equations”, *Applied
Mathematics and Computation*, Vol. 88 Nos. 2/3, pp. 131-5.

Adomian, G. (1997d), “On the dynamics of a reaction-diffusion system”,
*Applied Mathematics and Computation*, Vol. 81 No. 1, pp. 93-5.

Adomian, G. (1997e), “Optical propagation in random media”, *Applied
Mathematics and Computation*, Vol. 88 Nos. 2/3, pp. 127-9.

Adomian, G. (1998a), “Analytic solution of nonlinear integral equations
of Hammerstein type”, *Applied Mathematics Letters*, Vol. 11 No. 3,
pp. 127-30.

Adomian, G. (1998b), “Nonlinear dissipative wave equations”, *Applied
Mathematics Letters*, Vol. 11 No. 3, pp. 125-6.

Adomian, G. (1998c), “Solution of the Thomas-Fermi equation”, *Applied
Mathematics Letters*, Vol. 11, No. 3, pp. 131-3.

Adomian, G. (1998d), “Solutions of nonlinear P.D.E.”, *Applied
Mathematics Letters*, Vol. 11 No. 3, pp. 121-3.

Adomian, G. and Adomian, G.E. (1984), “A global method for solution of
complex systems”, *Mathematical Modelling*, Vol. 5 No. 4, pp.
251-63.

Adomian, G. and Adomian, G.E. (1985), “Cellular systems and aging
models”, *Computers and Mathematics with Applications*, Vol. 11 Nos.
1/3, pp. 283-91.

Adomian, G. and Adomian, G.E. (1986), “Solution of the Marchuk model of
infectious disease and immune response”, *Mathematical Modelling*,
Vol. 7 Nos 5/8, pp. 803-7.

Adomian, G., Adomian, G.E. and Bellman, R.E. (1984), “Biological system
interactions”, *Proceedings of the National Academy of Sciences of the
United States of America*, Vol. 81 No. 9, pp. 2938-40.

Adomian, G. and Bellman, R.E. (1982), “On the Itô equation”,
*Journal of Mathematical Analysis and Applications*, Vol. 86 No. 2, pp.
476-8.

Adomian, G. and Bellomo, N. (1986), “On the Tricomi problem”, *Computers
and Mathematics with Applications*, Vol. 12 Nos 4/5, Pt. A, pp. 557-63.

Adomian, G., Bellomo, N. and Riganti, R. (1983), “Semilinear stochastic
systems: analysis with the method of the stochastic Green’s function and
application in mechanics”, *Journal of Mathematical Analysis and
Applications*, Vol. 96 No. 2, pp. 330-40.

Adomian, G., Bigi, D. and Riganti, R. (1985), “On the solutions of
stochastic initial-value problems in continuum mechanics”, *Journal of
Mathematical Analysis and Applications*, Vol. 110 No. 2, pp. 442-62.

Adomian, G., Cherruault, Y. and Abbaoui, K. (1996), “A nonperturbative
analytical solution of immune response with time-delays and possible
generalization”, *Mathematical and Computer Modelling*, Vol. 24 No.
10, pp. 89-96.

Adomian, G. and Efinger, H.J. (1994), “Analytic solutions for
time-dependent Schrödinger equations with linear or nonlinear Hamiltonians”,
*Foundations of Physics Letters*, Vol. 7 No. 5, pp. 489-91.

Adomian, G. and Elrod, M. (1981), “Generation of a stochastic process
with desired first- and second-order statistics”, *Kybernetes*, Vol.
10 No. 1, pp. 25-30.

Adomian, G., Elrod, M. and Rach, R. (1989), “A new approach to boundary
value equations and application to a generalization of Airy’s equation”,
*Journal of Mathematical Analysis and Applications*, Vol. 140 No. 2, pp.
554-68.

Adomian, G. and Lynch, T. (1977), “Stochastic differential operator
equations with random initial conditions”, *Journal of Mathematical
Analysis and Applications*, Vol. 61 No. 1, pp. 216-26.

Adomian, G. and Malakian, K. (1979), “Closure approximation error in
the mean solution of stochastic differential equations by the hierarchy method”,
*Journal of Statistical Physics*, Vol. 21 No. 2, pp. 181-9.

Adomian, G. and Malakian, K. (1980a), “Operator-theoretic solution of
stochastic systems”, *Journal of Mathematical Analysis and Applications*,
Vol. 76 No. 1, pp. 183-201.

Adomian, G. and Malakian, K. (1980b), “Inversion of stochastic partial
differential operators – the linear case”, *Journal of
Mathematical Analysis and Applications*, Vol. 77 No. 2, pp. 505-12.

Adomian, G. and Malakian, K. (1980c), “Self-correcting approximate
solution by the iterative method for linear and nonlinear stochastic
differential equations”, *Journal of Mathematical Analysis and
Applications*, Vol. 76 No. 2, pp. 309-27.

Adomian, G. and Malakian, K. (1980d), “Stochastic analysis”, *Mathematical
Modelling*, Vol. 1 No. 3, pp. 211-35.

Adomian, G. and Malakian, K. (1981), “A comparison of the iterative
method and Picard’s successive approximations for deterministic and
stochastic differential equations, *Applied Mathematics and Computation*,
Vol. 8 No. 3, pp. 187-204.

Adomian, G. and Malakian, K. (1982), “Existence and uniqueness of
statistical measures for solution processes for linear-stochastic differential
equations”, *Journal of Mathematical Analysis and Applications*,
Vol. 89 No. 1, pp. 186-92.

Adomian, G. and Malakian, K. (1986), “Existence of the inverse of a
linear stochastic operator”, *Journal of Mathematical Analysis and
Applications*, Vol. 114 No. 1, pp. 55-6.

Adomian, G. and Meyers, R.E. (1993), “Nonlinear transport in moving
fluids”, *Applied Mathematics Letters*, Vol. 6 No. 5, pp. 35-8.

Adomian, G. and Meyers, R.E. (1995a), “Generalized nonlinear Schrödinger
equation with time-dependent dissipation”, *Applied Mathematics Letters*,
Vol. 8 No. 6, pp. 7-8.

Adomian, G. and Meyers, R.E. (1995b), “Isentropic flow of an inviscid
gas”, *Applied Mathematics Letters*, Vol. 8 No. 1, pp. 43-6.

Adomian, G. and Meyers, R.E. (1995c), “The Ginzburg-Landau equation”,
*Computers and Mathematics with Applications*, Vol. 29 No. 3, pp. 3-4.

Adomian, G., Pandolfi, M. and Rach, R. (1988), “An application of the
decomposition method to the matrix Riccati equation in a neutron transport
process”, *Journal of Mathematical Analysis and Applications*, Vol.
136 No. 2, pp. 557-67.

Adomian, G. and Rach, R. (1983a), “Inversion of nonlinear stochastic
operators”, *Journal of Mathematical Analysis and Applications*,
Vol. 91 No. 1, pp. 39-46.

Adomian, G. and Rach, R. (1983b), “Anharmonic oscillator systems”,
*Journal of Mathematical Analysis and Applications*, Vol. 91 No. 1, pp.
229-36.

Adomian, G. and Rach, R. (1983c), “A nonlinear differential delay
equation”, *Journal of Mathematical Analysis and Applications*, Vol.
91 No. 2, pp. 301-4.

Adomian, G. and Rach, R. (1983d), “Nonlinear stochastic differential
delay equations”, *Journal of Mathematical Analysis and Applications*,
Vol. 91 No. 1, pp. 94-101.

Adomian, G. and Rach, R. (1984a), “Light scattering in crystals”,
*Journal of Applied Physics*, Vol. 56 No. 9, pp. 2592-4.

Adomian, G. and Rach, R. (1984b), “On nonzero initial conditions in
stochastic differential equations”, *Journal of Mathematical Analysis
and Applications*, Vol. 102 No. 2, pp. 363-4.

Adomian, G. and Rach, R. (1985a), “Algebraic equations with exponential
terms”, *Journal of Mathematical Analysis and Applications*, Vol.
112 No. 1, pp. 136-40.

Adomian, G. and Rach, R. (1985b), “Application of the decomposition
method to inversion of matrices”, *Journal of Mathematical Analysis and
Applications*, Vol. 108 No. 2, pp. 409-21.

Adomian, G. and Rach, R. (1985c) “An algorithm for transient dynamic
analysis”, *Transactions of the Society for Computer Simulation*,
Vol. 2 No. 4, pp. 321-7.

Adomian, G. and Rach, R. (1985d), “Coupled differential equations and
coupled boundary conditions”, *Journal of Mathematical Analysis and
Applications*, Vol. 112 No. 1, pp. 129-35.

Adomian, G. and Rach, R. (1985e), “Nonlinear differential equations
with negative power nonlinearities”, *Journal of Mathematical Analysis
and Applications*, Vol. 112 No. 2, pp. 497-501.

Adomian, G. and Rach, R. (1985f), “Nonlinear plasma response”, *Journal
of Mathematical Analysis and Applications*, Vol. 111 No. 1, pp. 114-8.

Adomian, G. and Rach, R. (1985g), “On the solution of algebraic
equations by the decomposition method”, *Journal of Mathematical
Analysis and Applications*, Vol. 105 No. 1, pp. 141-66.

Adomian, G. and Rach, R. (1985h), “Polynomial nonlinearities in
differential equations”, *Journal of Mathematical Analysis and
Applications*, Vol. 109 No. 1, pp. 90-5.

Adomian, G. and Rach, R. (1986a), “On the solution of nonlinear
differential equations with convolution product nonlinearities”, *Journal
of Mathematical Analysis and Applications*, Vol. 114 No. 1, pp. 171-5.

Adomian, G. and Rach, R. (1986b), “A coupled nonlinear system”,
*Journal of Mathematical Analysis and Applications*, Vol. 113 No. 2, pp.
510-3.

Adomian, G. and Rach, R. (1986c), “A new computational approach for
inversion of very large matrices”, *Mathematical Modelling*, Vol. 7
Nos. 2/3, pp. 113-41.

Adomian, G. and Rach, R. (1986d), “Algebraic computation and the
decomposition method”, *Kybernetes*, Vol. 15 No. 1, pp. 33-7.

Adomian, G. and Rach, R. (1986e), “On composite nonlinearities and the
decomposition method”, *Journal of Mathematical Analysis and
Applications*, Vol. 113 No. 2, pp. 504-9.

Adomian, G. and Rach, R. (1986f), “On linear and nonlinear
integro-differential equations”, *Journal of Mathematical Analysis and
Applications*, Vol. 113 No. 1, pp. 199-201.

Adomian, G. and Rach, R. (1986g), “Solving nonlinear differential
equations with decimal power nonlinearities”, *Journal of Mathematical
Analysis and Applications*, Vol. 114 No. 2, pp. 423-5.

Adomian, G. and Rach, R. (1986h), “The noisy convergence phenomena in
decomposition method solutions”, *Journal of Computational and Applied
Mathematics*, Vol. 15 No. 3, pp. 379-81.

Adomian, G. and Rach, R. (1987), “Explicit solutions for differential
equations”, *Applied Mathematics and Computation*, Vol. 23 No. 1,
pp. 49-59.

Adomian, G. and Rach, R. (1988), “Evaluation of integrals by
decomposition”, *Journal of Computational and Applied Mathematics*,
Vol. 23 No. 1, pp. 99-101.

Adomian, G. and Rach, R. (1989), “Analytic parametrization and the
decomposition method”, *Applied Mathematics Letters*, Vol. 2 No. 4,
pp. 311-3.

Adomian, G. and Rach, R., (1990a) “Equality of partial solutions in the
decomposition method for linear or nonlinear partial differential equations”,
*Computers and Mathematics with Applications*, Vol. 19 No. 12, pp. 9-12.

Adomian, G. and Rach, R. (1990b), “Purely nonlinear differential
equations”, *Computers and Mathematics with Applications*, Vol. 20
No. 1, pp. 1-3.

Adomian, G. and Rach, R. (1991a), “Linear and nonlinear Schrödinger
equations”, *Foundations of Physics*, Vol. 21 No. 8, pp. 983-91.

Adomian, G. and Rach, R. (1991b), “Solution of nonlinear ordinary and
partial differential equations of physics”, *Journal of Mathematical and
Physical Sciences*, Vol. 25 Nos 5/6, pp. 703-18.

Adomian, G. and Rach, R. (1991c), “Transformation of series”, *Applied
Mathematics Letters*, Vol. 4 No. 4, pp. 69-71.

Adomian, G. and Rach, R. (1992a), “A further consideration of partial
solutions in the decomposition method”, *Computers and Mathematics with
Applications*, Vol. 23 No. 1, pp. 51-64.

Adomian, G. and Rach, R. (1992b), “An approach to steady-state
solutions”, *Applied Mathematics Letters*, Vol. 5 No. 5, pp. 39-40.

Adomian, G. and Rach, R. (1992c), “Generalization of Adomian
polynomials to functions of several variables”, *Computers and
Mathematics with Applications*, Vol. 24 Nos. 5/6, pp. 11-24.

Adomian, G. and Rach, R. (1992d), “Inhomogeneous nonlinear partial
differential equations with variable coefficients”, *Applied Mathematics
Letters*, Vol. 5 No. 2, pp. 11-2.

Adomian, G. and Rach, R. (1992e), “Modified decomposition solution of
nonlinear partial differential equations”, *Applied Mathematics Letters*,
Vol. 5 No. 6, pp. 29-30.

Adomian, G. and Rach, R. (1992f), “Noise terms in decomposition
solution series”, *Computers and Mathematics with Applications*,
Vol. 24 No. 11, pp. 61-4.

Adomian, G. and Rach, R. (1992g), “Nonlinear transformation of series
– Part II”, *Computers and Mathematics with Applications*,
Vol. 23 No. 10, pp. 79-83.

Adomian, G. and Rach, R. (1993a) “A new algorithm for matching boundary
conditions in decomposition solutions”, *Applied Mathematics and
Computation*, Vol. 58 No. 1, pp. 61-8.

Adomian, G. and Rach, R. (1993b) “Analytic solution of nonlinear
boundary-value problems in several dimensions by decomposition”, *Journal
of Mathematical Analysis and Applications*, Vol. 174 No. 1, pp. 118-37.

Adomian, G. and Rach, R. (1993c) “Solution of nonlinear partial
differential equations in one, two, three and four dimensions”, *World
Scientific Series in Applicable Analysis*, Vol. 2, pp. 1-13.

Adomian, G. and Rach, R. (1994a), “A new algorithm for solution of the
harmonic oscillator by decomposition”, *Applied Mathematics Letters*,
Vol. 7 No. 1, pp. 53-6.

Adomian, G. and Rach, R. (1994b), “Modified decomposition solution of
linear and nonlinear boundary-value problems”, *Nonlinear Analysis,
Theory, Methods and Applications*, Vol. 23 No. 5, pp. 615-9.

Adomian, G. and Rach, R. (1995), “Kuramoto-Sivashinsky equation”,
*Journal of Applied Science and Computations*, Vol. 1 No. 3, pp. 476-80.

Adomian, G. and Rach, R. (1996), “Modified Adomian polynomials”,
*Mathematical and Computer Modelling*, Vol. 24 No. 11, pp. 39-46.

Adomian, G., Rach, R. and Elrod, M. (1988), “The decomposition method
applied to stiff systems”, *Mathematics and Computers in Simulation*,
Vol. 30 No. 3, pp. 271-6.

Adomian, G., Rach, R. and Elrod, M. (1989), “On the solution of partial
differential equations with specified boundary conditions”, *Journal of
Mathematical Analysis and Applications*, Vol. 140 No. 2, pp. 569-81.

Adomian, G., Rach, R. and Meyers, R.E. (1991a), “An efficient
methodology for the physical sciences”, *Kybernetes*, Vol. 20 No. 7,
pp. 24-34.

Adomian, G., Rach, R. and Meyers, R.E. (1991b), “Numerical algorithms
and decomposition”, *Computers and Mathematics with Applications*,
Vol. 22 No. 8, pp. 57-61.

Adomian, G., Rach, R. and Meyers, R.E. (1994), “Solution of generic
nonlinear oscillators”, *Applied Mathematics and Computation*, Vol.
64 Nos 2/3, pp. 167-70.

Adomian, G., Rach, R. and Meyers, R.E. (1997), “Numerical integration,
analytic continuation and decomposition”, *Applied Mathematics and
Computation*, Vol. 88 Nos 2/3, pp. 95-116.

Adomian, G., Rach, R. and Sarafyan, D. (1985), “On the solution of
equations containing radicals by the decomposition method”, *Journal of
Mathematical Analysis and Applications*, Vol. 111 No. 2, pp. 423-6.

Adomian, G., Rach, R. and Shawagfeh, N.T. (1995), “On the analytic
solution of the Lane-Emden equation”, *Foundations of Physics Letters*,
Vol. 8 No. 2, pp. 161-81.

Adomian, G. and Sarafyan, D. (1981), “Numerical solution of
differential equations in the deterministic limit of stochastic theory”,
*Applied Mathematics and Computation*, Vol. 8 No. 2, pp. 111-9.

Adomian, G. and Serrano, S.E. (1998), “Stochastic contaminant transport
equation in porous media”, *Applied Mathematics Letters*, Vol. 11
No. 1, pp. 53-5.

Adomian, G. and Sibul, L.H. (1971), “Propagation in stochastic media”,
*Proceedings of the 1971 Antennas and Propagation Society International
Symposium, Vol. 9*, IEEE, pp. 163-5, doi:10.1109/APS.1971.1150900.

Adomian, G. and Sibul, L.H. (1977), “Stochastic Green’s formula
and application to stochastic differential equations”, *Journal of
Mathematical Analysis and Applications*, Vol. 60 No. 3, pp. 743-6.

Adomian, G. and Sibul, L.H. (1981a), “On the control of stochastic
systems”, *Journal of Mathematical Analysis and Applications*, Vol.
83 No. 2, pp. 611-21.

Adomian, G. and Sibul, L.H. (1981b), “Symmetrized solutions for
nonlinear stochastic differential equations”, *International Journal of
Mathematics and Mathematical Sciences*, Vol. 4 No. 3, pp. 529-42,
doi:10.1155/S0161171281000380.

Adomian, G., Sibul, L.H. and Rach, R. (1983), “Coupled nonlinear
stochastic differential equations”, *Journal of Mathematical Analysis
and Applications*, Vol. 92 No. 2, pp. 427-34.

Adomian, G. and Vasudevan, R. (1984), “A stochastic approach to inverse
scattering in geophysical layers”, *Mathematical Modelling*, Vol. 5
No. 5, pp. 339-42.

Adomian, G. and Witten, M. (1994), “Computation of solutions to the
generalized Michaelis-Menton equation”, *Applied Mathematics Letters*,
Vol. 7 No. 4, pp. 45-8.

Afrouzi, G.A. and Khademloo, S. (2006), “On Adomian decomposition
method for solving reaction diffusion equation”, *International Journal
of Nonlinear Science*, Vol. 2 No. 1, pp. 11-5, available at: www.worldacademicunion.com/journal/1749-3889-3897IJNS/IJNSVol2No1Paper2.pdf

Alabdullatif, M., Abdusalam, H.A. and Fahmy, E.S. (2007), “Adomian
decomposition method for nonlinear reaction diffusion system of Lotka-Volterra
type”, *International Mathematical Forum*, Vol. 2 No. 2, pp. 87-96,
available at: www.m-hikari.com/imf-password2007/1-4-2007/abdusalamIMF1-4-2007.pdf

Al-Bayati, A.Y., Al-Sawoor, A.J. and Samarji, M.A. (2009), “A
multistage Adomian decomposition method for solving the autonomous van der Pol
system”, *Australian Journal of Basic and Applied Sciences*, Vol. 3
No. 4, pp. 4397-407.

Al-Dosary, K.I., Al-Jubouri, N.K. and Abdullah, H.K. (2008), “On the
solution of Abel differential equation by Adomian decomposition method”,
*Applied Mathematical Sciences*, Vol. 2, No. 43, 2105-18.

Alharbi, A. and Fahmy, E.S. (2010), “ADM-Padé solutions for
generalized Burgers and Burgers-Huxley systems with two coupled equations”,
*Journal of Computational and Applied Mathematics*, Vol. 233 No. 8, pp.
2071-80.

Al-Hayani, W. (2011), “Adomian decomposition method with Green’s
function for sixth-order boundary value problems”, *Computers and
Mathematics with Applications*, Vol. 61 No. 6, pp. 1567-75.

Al-Hayani, W. and Casasús, L. (2005a), “Approximate analytical
solution of fourth order boundary value problems”, *Numerical Algorithms*,
Vol. 40 No. 1, pp. 67-78.

Al-Hayani, W. and Casasús, L. (2005b), “The Adomian decomposition
method in turning point problems”, *Journal of Computational and Applied
Mathematics*, Vol. 177 No. 1, pp. 187-203.

Al-Hayani, W. and Casasús, L. (2006), “On the applicability of the
Adomian method to initial value problems with discontinuities”, *Applied
Mathematics Letters*, Vol. 19 No. 1, pp. 22-31.

Al-Humedi, H.O. and Ali, A.H. (2008), “Application of Adomian
decomposition method to solve Fisher’s equation”, *Journal of
Basrah Researches (Sciences)*, Vol. 35, pp. 23-32.

Al-Humedi, H.O. and Al-Qatrany, F.L.H. (2010), “Modified algorithm to
compute Adomian’s polynomials for solving non-linear systems of partial
differential equations”, *International Journal of Contemporary
Mathematical Sciences*, Vol. 5 No. 51, pp. 2505-21, available at: www.m-hikari.com/ijcms-2010/49-52-2010/odaIJCMS49-52-2010.pdf

Ali, A.H. and Al-Saif, A.S.J. (2008), “Adomian decomposition method for
solving some models of nonlinear partial differential equations”, *Basrah
Journal of Science (A)*, Vol. 26 No. 1, pp. 1-11.

Alizadeh, E., Sedighi, K., Farhadi, M. and Ebrahimi-Kebria, H.R. (2009),
“Analytical approximate solution of the cooling problem by Adomian
decomposition method”, *Communications in Nonlinear Science and
Numerical Simulation*, Vol. 14 No. 2, pp. 462-72.

Al-Khaled, K. and Allan, F. (2004), “Construction of solutions for the
shallow water equations by the decomposition method”, *Mathematics and
Computers in Simulation*, Vol. 66 No. 6, pp. 479-86.

Al-Khaled, K., Kaya, D. and Noor, M.A. (2004), “Numerical comparison of
methods for solving parabolic equations”, *Applied Mathematics and
Computation*, Vol. 157 No. 3, pp. 735-43.

Al-Khawaja, U. and Al-Khaled, K. (2007), “Error control in Adomian’s
decomposition method applied to the time-dependent Gross-Pitaevskii equation”,
*International Journal of Computer Mathematics*, Vol. 84 No. 1, pp. 81-7.

Al-Kurdi, A. and Mulhem, S. (2011), “Solution of twelfth order boundary
value problems using Adomian decomposition method”, *Journal of Applied
Sciences Research*, Vol. 7 No. 6, pp. 922-34, available at: www.aensionline.com/jasr/jasr/2011/922-934.pdf

Al-Mazmumy, M.A., “Adomian decomposition method for solving Goursat’s
problems” (2011), *SR (Scientific Research) Applied Mathematics*,
Vol. 2 No. 8, pp. 975-80, doi:10.4236/am.2011.28134

Aly, E.H., Ebaid, A. and Rach, R. (2012), “Advances in the Adomian
decomposition method for solving two-point nonlinear boundary value problems
with Neumann boundary conditions”, *Computers and Mathematics with
Applications*, Vol. 63 No. 6, pp. 1056-65.

Amani, A.R. and Sadeghi, J. (2008), “Adomian decomposition method and
two coupled scalar fields”, Balan, V. (Ed.), in *Balkan Society of
Geometers (BSG) Proceedings of the 15th International Conference on “Differential
Geometry and Dynamical Systems” (DGDS-2007), Bucharest, Romania, October
5-7, 2007,* Geometry Balkan Press, Bucharest, Romania, pp. 11*-*18,
available at: www.mathem.pub.ro/proc/bsgp-15/P-AM.pdf

Andrianov, I.V., Olevskii, V.I. and Tokarzewski, S. (1998), “A modified
Adomian’s decomposition method”, *Journal of Applied Mathematics
and Mechanics*, Vol. 62 No. 2, pp. 309-14.

Arenas, A.J., González-Parra, G., Jódar, L. and Villanueva, R.J.
(2009), “Piecewise finite series solution of nonlinear initial value
differential problem”, *Applied Mathematics and Computation*, Vol.
212 No. 1, pp. 209-15.

Arora, H. and Abdelwahid, F. (1993), “Solution of non-integer order
differential equations via the Adomian decomposition method”, *Applied
Mathematics Letters*, Vol. 6 No. 1, pp. 21-3.

Aslanov, A. (2009), “Approximate solutions of Emden-Fowler type
equations”, *International Journal of Computer Mathematics*, Vol. 86
No. 5, pp. 807-826.

Arslanturk, C. (2005), “A decomposition method for fin efficiency of
convective straight fins with temperature-dependent thermal conductivity”,
*International Communications in Heat and Mass Transfer*, Vol. 32 No. 6,
pp. 831-41.

Asil, V., Bulut, H. and Evans, D.J. (2004), “On the oscillatory
solutions of nonlinear hyperbolic differential equations by the decomposition
method”, *International Journal of Computer Mathematics*, Vol. 81
No. 5, pp. 639-45.

Asil, V., Bulut, H. and Evans, D.J. (2005), “The Adomian decomposition
method for the approximate solution of homogeneous differential equations with
dual variable and dual coefficients”, *International Journal of Computer
Mathematics*, Vol. 82 No. 8, pp. 977-86.

Aslanov, A. and Abu-Alshaikh, I. (2008), “Further developments to the
decomposition method for solving singular initial-value problems”, *Mathematical
and Computer Modelling*, Vol. 48 Nos 5/6, pp. 700-11.

Attili, B.S. (2005), “The Adomian decomposition method for computing
eigenelements of Sturm-Liouville two point boundary value problems”, *Applied
Mathematics and Computation*, Vol. 168 No. 2, pp. 1306-16.

Attili, B.S. and Lesnic, D. (2006), “An efficient method for computing
eigenelements of Sturm-Liouville fourth-order boundary value problems”, *Applied
Mathematics and Computation*, Vol. 182 No. 2, pp. 1247-54.

Azreg-Aïnou, M. (2009), “A developed new algorithm for evaluating
Adomian polynomials”, *CMES: Computer Modeling in Engineering and
Sciences*, Vol. 42 No. 1, pp. 1-18.

Azreg-Aïnou, M. (2010), “Developed Adomian method for quadratic
Kaluza-Klein relativity”, *Classical and Quantum Gravity*, Vol. 27
No. 1, doi:10.1088/0264-9381/27/1/015012.

Az-Zo’bi, E.A. and Al-Khaled, K. (2010), “A new convergence proof
of the Adomian decomposition method for a mixed hyperbolic elliptic system of
conservation laws”, *Applied Mathematics and Computation*, Vol. 217
No. 8, pp. 4248-56.

Babajee, D.K.R., Dauhoo, M.Z., Darvishi, M.T., and Barati, A. (2008), “A
note on the local convergence of iterative methods based on Adomian
decomposition method and 3-node quadrature rule”, *Applied Mathematics
and Computation*, Vol. 200 No. 1, pp. 452-8.

Babolian, E. and Biazar, J. (2002a), “On the order of convergence of
Adomian method”, *Applied Mathematics and Computation*, Vol. 130
Nos. 2/3, pp. 383-7.

Babolian, E. and Biazar, J. (2002b) “Solution of nonlinear equations by
modified Adomian decomposition method”, *Applied Mathematics and
Computation*, Vol. 132 No. 1, pp. 167-72.

Babolian, E. and Biazar, J. (2002c), “Solving the problem of biological
species living together by Adomian decomposition method”, *Applied
Mathematics and Computation*, Vol. 129 Nos 2/3, pp. 339-43.

Babolian, E. and Biazar, J. (2003), “Solving concrete examples by
Adomian method”, *Applied Mathematics and Computation*, Vol. 135 No.
1, pp. 161-7.

Babolian, E., Biazar, J. and Vahidi, A.R. (2004a), “A new computational
method for Laplace transforms by decomposition method”, *Applied
Mathematics and Computation*, Vol. 150 No. 3, pp. 841-6.

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Wazwaz, A.-M. (2001n), “Analytic treatment for variable coefficient
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Wazwaz, A.-M. (2002a), “A new method for solving singular initial value
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Wazwaz, A.-M. (2002b), “A reliable treatment for mixed
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Wazwaz, A.-M. (2002c), “The numerical solution of special fourth-order
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Wazwaz, A.-M. (2002d), “Exact solutions for variable coefficients
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Wazwaz, A.-M. (2002e), *Partial Differential Equations: Methods and
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Wazwaz, A.-M. (2003a), “An analytic study on the third-order dispersive
partial differential equations”, *Applied Mathematics and Computation*,
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Wazwaz, A.-M. (2003b), “The existence of noise terms for systems of
inhomogeneous differential and integral equations”, *Applied Mathematics
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Wazwaz, A.-M. (2004), “The existence of noise terms for systems of
inhomogeneous differential and integral equations”, *Applied Mathematics
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Wazwaz, A.-M. (2005a), “Adomian decomposition method for a reliable
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Wazwaz, A.-M. (2005b), “Adomian decomposition method for a reliable
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Wazwaz, A.-M. (2005c), “Analytical solution for the time-dependent
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Wazwaz, A.-M. (2005d), “The modified decomposition method for analytic
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Wazwaz, A.-M. (2006a), “A comparison study between the modified
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Wazwaz, A.-M. (2006b), “Padé approximants and Adomian
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Wazwaz, A.-M. (2006c), “The modified decomposition method and Padé
approximants for a boundary layer equation in unbounded domain”, *Applied
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Wazwaz, A.-M. (2006d), “The modified decomposition method for analytic
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Wazwaz, A.-M. (2007), “A comparison between the variational iteration
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Wazwaz, A.-M. (2009), *Partial Differential Equations and Solitary Waves
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Wazwaz, A.-M. (2010), “The combined Laplace transform-Adomian
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Wazwaz, A.-M. (2011a), “The regularization method for Fredholm integral
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Wazwaz, A.-M. and El-Sayed, S.M. (2001), “A new modification of the
Adomian decomposition method for linear and nonlinear operators”, *Applied
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Wazwaz, A.-M. and Gorguis, A. (2004a), “An analytic study of Fisher’s
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Wazwaz, A.-M. and Gorguis, A. (2004b), “Exact solutions for heat-like
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**Further reading**

Adomian, G. (1983), *Stochastic Systems*, Academic Press, New York,
NY.

Adomian, G. (1986), *Nonlinear Stochastic Operator Equations*,
Academic Press, Orlando, FL.

(1987),

Adomian, G. (1989), *Nonlinear Stochastic Systems Theory and Applications
to Physics*, Kluwer Academic Publishers, Dordrecht.

Adomian, G. (1994), *Solving Frontier Problems of Physics: The
Decomposition Method*, Kluwer Academic Publishers, Dordrecht.

Bellman, R.E. and Adomian, G. (1985), *Partial Differential Equations: New
Methods for their Treatment and Solution*, D. Reidel Publishing Co.,
Dordrecht, pp. 237-87.

Bellomo, N. and Riganti, R. (1987), *Nonlinear Stochastic System Analysis
in Physics and Mechanics*, World Scientific Publishing Co., Singapore and
River Edge, NJ.

Cherruault, Y. (1998), *Modèles et méthodes mathématiques
pour les sciences du vivant*, Presses Universitaires de France, Paris, pp.
119-61, 256-64.

Grzymkowski, R. (2010), *Nieklasyczne metody rozwięzywania zagadnień
przewodzenia ciepła*, Wydawnictwo Politechniki Ślęskiej,
Gliwice, pp. 142-87.

Grzymkowski, R., Hetmaniok, E. and Słota, D. (2002), *Wybrane metody
obliczeniowe w rachunku wariacyjnym oraz w równaniach róóniczkowych
i całkowych*, Wydawnictwo Pracowni Komputerowej Jacka Skalmierskiego,
Gliwice, pp. 173-246.

Serrano, S.E. (1997), *Hydrology for Engineers, Geologists and
Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and
Contaminant Hydrology*, HydroScience Inc., Lexington, KY.

Serrano, S.E. (2001), *Engineering Uncertainty and Risk Analysis: A
Balanced Approach to Probability, Statistics, Stochastic Modeling, and
Stochastic Differential Equations*, HydroScience Inc., Lexington, KY.

Serrano, S.E. (2010), *Hydrology for Engineers, Geologists, and
Environmental Professionals: An Integrated Treatment of Surface, Subsurface, and
Contaminant Hydrology*, 2nd revised ed., HydroScience Inc., Ambler, PA.

Serrano, S.E. (2011), *Engineering Uncertainty and Risk Analysis: A
Balanced Approach to Probability, Statistics, Stochastic Processes, and
Stochastic Differential Equations*, 2nd revised ed., HydroScience Inc.,
Ambler, PA.

Shingareva, I. and Lizárraga-Celaya, C. (2011), *Solving Nonlinear
Partial Differential Equations with Maple and Mathematica*, Springer, New
York, NY, pp. 227-42.

Wazwaz, A.-M. (1997), *A First Course in Integral Equations*, World
Scientific Publishing Co., Singapore and River Edge, NJ.

Wazwaz, A.-M. (2002), *Partial Differential Equations: Methods and
Applications*, A.A. Balkema, Lisse.

Wazwaz, A.-M. (2009), *Partial Differential Equations and Solitary Waves
Theory*, Higher Education Press, Beijing, and Springer, Berlin.

Wazwaz, A.-M. (2011), *Linear and Nonlinear Integral Equations: Methods
and Applications*, Higher Education Press, Beijing and Springer, Berlin.

**Randolph Rach***316, South Naple Street, Hartford,
Michigan 49057-1225, USA E-mail:* *tapstrike@triton.net*

**Acknowledgments**

The author is grateful to the Adomian family for their kindness and
particularly would like to thank Mrs Corinne Adomian, Mrs Laura Adomian David
and Mr William David, Athens, Georgia, USA for their generous assistance with
access to Professor George Adomian’s extensive files to locate copies of
his publications through the years. The author also appreciates the generous
assistance from his friends and colleagues in locating research papers on the
theory and applications of the Adomian decomposition method to enhance this
developing worldwide, constructive bibliography, including especially Dr
Abdul-Majid Wazwaz, Saint Xavier University, Chicago, Illinois, USA, Dr Sergio
E. Serrano, Temple University, Philadelphia, Pennsylvania, USA, Dr Jun-Sheng
Duan, Shanghai Institute of Technology, Shanghai, China, Dr Yan-Ping Sun,
Taiyuan University of Technology, Taiyuan, China, Dr Yezhi Lin, East China
Normal University, Shanghai, China, Dr Mehdi Dehghan, Amirkabir University of
Technology, Tehran, Iran, Dr Daniel Lesnic, University of Leeds, Leeds, UK, Dr
Damian Słota, Silesian University of Technology, Gliwice, Poland, Dr Luis
Casasús and Dr Waleed Al-Hayani, Polytechnic University of Madrid, Madrid,
Spain, Dr Paulo Rebelo, University of Beira Interior, Covilhã, Portugal and
Dr José M. Machado, São Paulo State University, São José do
Rio Preto, Brazil. *Feci quod potui, faciant meliora potentes.*

**About the author**

Randolph Rach is retired and formerly a Senior Engineer at Microwave Laboratories Inc. His experience includes research and development in microwave electronics and travelling-wave tube technology. He has both authored and co-authored 76 papers in applied mathematics and is an early contributor to the Adomian decomposition method. His current research interests include nonlinear systems analysis, nonlinear ordinary and partial differential equations, nonlinear integral equations, and nonlinear boundary value problems. Randolph Rach can be contacted at: tapstrike@triton.net