... the differential operator is modified with one additional term which takes into account the effect of boundary conditions. Then the new problem can be directly integrated in the same way as an ordinary differential equation. In this work Adomian's decomposition method with analytic extension is used to obtain...

...Antonio García‐Olivares Adomian's method is completed to obtain the analytic solution of any partial differential equation with boundary conditions defined on the four sides of a rectangle. Adomian's decomposition method is first used to obtain the N‐order approximant to the one direction partial...

...Y. Cherruault; M. Inc; K. Abbaoui The Adomian decomposition method is used to implement the non‐linear Korteweg–de Vries equations. The analytic solution of the equation is calculated in the form of a convergent power series with easily computable components. The non‐homogeneous problem is quickly...

...S. Khelifa; 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 curves. Outlines the new approach and provides applications of its use. Let S...

...M. Inc; Y. Cherruault We use the Adomian decomposition method to study a non‐linear diffusion‐convection problem (NDCP). The decomposition method has been applied recently to a wide class of non‐linear stochastic and deterministic operator equations involving algebraic, differential, integro...

..., Lorentz’s equation and Edem’s equation are given and solved. In this work, the general equation given by ∂ p \over ∂ t = (∇ ⋅(q(x)⋅ ∇p)) + f(x, t) is solved by using decomposition methods, and is compared to other techniques. This equation can be used...

...S. Khelifa; Y. Cherruault Describes the Adomian decomposition method and provides a new proof for the evaluation of the Abbaoui‐Cherruault numbers. Demonstrates a new result for Bell polynominals and establishes and proves a new norm bound for Adomian polynominals. Demonstrates an application...

...; _{n) © MCB UP Limited 1999 Decomposition method Integral transforms Cybernetics In the 1980s, Adomian proposed a new and ingenious method for exactly solving nonlinear functional equations of various kinds (Adomian, 1994) (algebraic, differential, partial, integral, etc}...

... the A_n are functions called Adomian’s polynomials. The A_n are obtained by writing: (1.3) The operator N is decomposed as follows: (1.2) The decomposition method (Cherruault, 1998) consists in looking for a solution in the form: where N is an operator from...

... of an organ, varying from zero for an entirely damaged organ to unity for a healthy organ. © MCB UP Limited 1999 AIDS Cybernetics Decomposition method HIV Immune system Viruses Let us first describe the immuno‐genetical of antiviral immune response. Immune response to stimulants...

...K. Abbaoui; 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 formulation of the Adomain polynomials and we compare our technique with the Picard method...

... numerically by the decomposition method. © MCB UP Limited 1998 Boundary conditions Computational methods Cybernetics Decomposition method More than ten years ago, G. Adomian introduced a numerical technique in which informal mathematical calculations are used to solve physics problems...

...M. Hadizadeh; K. Maleknejad The Adomian decomposition method is used and applied to the mathematical model of a biosensor. This model consists of a heat equation with non‐linear and non‐local boundary conditions. To obtain a canonical form of Adomian, an equivalent non‐linear Volterra integral...

...(x,t)g(u(t))dt = f(x), (2) and without loss of generality, we can take a = 0. Let us consider the non‐linear integral equation: © MCB UP Limited 1997 Adomian’s polynomials Decomposition method Integral equations Perturbation...