Application of the SBA Method for Solving the Partial Differential Equation

In this paper, we will construct the solution of the Landau-Ginzburg equation by the Adomian decomposition method. This method avoids linearization of space and discretization of time, it often gives a good approximation of the exact solution.

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The aim of this paper is to solve analytically fluid flow problems in a porous medium, the Laplace-Adomian method gives algorhims that converge faster to achieve the exact solution when it exists.

Data on solving of nonlinear integro-differential equations using Laplace-SBA method are scarce. The objective of this paper is to determine exact solution of nonlinear 2 dimensionnal Voltera-Fredholm differential equation by this method. First, SBA method and Laplace SBA method are described. Second, three nonlinear Voolterra-Fredholm integro-differential equations are solved using each method. Application of each method give an exact solution. However, application of Laplace-SBA method permits for solve integro-differential equation compared with SBA method. This proves that this last method can be fruitfully applied in the resolution of integro-differential equations.