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Article
Publication date: 1 November 1995

K. Abbaoui, Y. Cherruault and M. Ndour

The decomposition method is used for solving differential systems in biology and medicine. A comparison is given between the Runge‐Kutta method and the decomposition…

Abstract

The decomposition method is used for solving differential systems in biology and medicine. A comparison is given between the Runge‐Kutta method and the decomposition technique. New relationships for calculating Adomian’s polynomials are used for solving the differential systems governing the competition between species and based on the Lotka‐Volterra model.

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Kybernetes, vol. 24 no. 8
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 June 1999

N. Himoun, K. Abbaoui and Y. Cherruault

New results about convergence of Adomian’s method are presented. This method was developed by G. Adomian for solving non‐linear functional equations of different kinds…

Abstract

New results about convergence of Adomian’s method are presented. This method was developed by G. Adomian for solving non‐linear functional equations of different kinds. New conditions for obtaining convergence of the decomposition series are given. In a similar way, the convergence of a regularisation method which can, for example, be applied to Fredholm integral equations of the first kind, is proved.

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Kybernetes, vol. 28 no. 4
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 June 1996

M. Ndour, K. Abbaoui, H. Ammar and Y. Cherruault

Describes the use of the decomposition method for solving the differential system governing the interaction between two species, based on the Lotka‐Volterra model. The…

Abstract

Describes the use of the decomposition method for solving the differential system governing the interaction between two species, based on the Lotka‐Volterra model. The Alienor method is applied for identifying the parameters of the model, which are the intrinsic rates of natural increase of the different species and their interaction coefficients.

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Kybernetes, vol. 25 no. 4
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 July 1999

T. Badredine, K. Abbaoui and Y. Cherruault

This paper deals with a new proof of convergence of Adomian’s method applied to nonlinear integral equations. By using a new formulation of Adomian’s polynomials, we give…

Abstract

This paper deals with a new proof of convergence of Adomian’s method applied to nonlinear integral equations. By using a new formulation of Adomian’s polynomials, we give the relation between the Picard method and Adomian’s technique.

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Kybernetes, vol. 28 no. 5
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 December 2000

R.Z. Ouedraogo, Y. Cherruault and K. Abbaoui

Considers the convergence of Adomian’s method applied to algebraic equations. Presents directly some conditions of convergence which only depend on the equations…

Abstract

Considers the convergence of Adomian’s method applied to algebraic equations. Presents directly some conditions of convergence which only depend on the equations’ coefficients and also gives an estimation of the truncation error together with some numerical applications.

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Kybernetes, vol. 29 no. 9/10
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 December 2001

K. Abbaoui, M.J. Pujol, Y. Cherruault, N. Himoun and P. Grimalt

A new approach of the decomposition method (Adomian) in which the Adomian scheme is obtained in a more natural way than in the classical presentation, is given. A new…

Abstract

A new approach of the decomposition method (Adomian) in which the Adomian scheme is obtained in a more natural way than in the classical presentation, is given. A new condition for obtaining convergence of the decomposition series is also included.

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Kybernetes, vol. 30 no. 9/10
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 February 1999

K. Abbaoui and Y. Cherruault

In this paper, we use the decomposition method for solving the Cauchy problem without using the canonical form of Adomian. We also give proof of convergence by using a new…

Abstract

In this paper, we use the decomposition method for solving the Cauchy problem without using the canonical form of Adomian. We also give proof of convergence by using a new formulation of the Adomain polynomials and we compare our technique with the Picard method.

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Kybernetes, vol. 28 no. 1
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 January 2004

M. Inc, Y. Cherruault and K. Abbaoui

Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is…

Abstract

Studies an analytic solution and a reliable numerical approximation of linear and non‐linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non‐homogeneous problem is quickly solved by observing the self‐cancelling “noise terms” where the sum of the components vanishes in the limit. Several linear or non‐linear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations.

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Kybernetes, vol. 33 no. 1
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 October 2000

Yves Cherruault

New methods for optimization and for solving nonlinear functional equations are given and are applied to the identification and optimal control of models coming from life sciences.

Abstract

New methods for optimization and for solving nonlinear functional equations are given and are applied to the identification and optimal control of models coming from life sciences.

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Kybernetes, vol. 29 no. 7/8
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 1 April 2002

S. Khelifa and Y. Cherruault

Aim's to show how to approach the solution for a class of first order p.d.e. using Adomian decomposition method. Discusses the generalities of the method and α‐dense…

Abstract

Aim's to show how to approach the solution for a class of first order p.d.e. using Adomian decomposition method. Discusses the generalities of the method and α‐dense curves. Outlines the new approach and provides applications of its use.

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Kybernetes, vol. 31 no. 3/4
Type: Research Article
ISSN: 0368-492X

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