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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.