Adomian Decomposition Method For Evolution Equations

Adomian decomposition method is an effective method to linear and nonlineardifferential equations without discretization. The explicit and numerical solutions ofthe equations are calculated in the form of the convergent power series with easilycomputable components. The essence of the decomposition method is that itdecompose the equation in several parts and then to solve the problem. It has somedistinct advantages in that it is adaptable to a rather wide class of differentialequations and it handle more easily for finding the exact and approximation solutions,so it has been receiving much attention especially in foreign countries. In this paper we apply Adomian decomposition scheme to solve the evolutionequations. The tests of the equations show the advantage of the decompositionmethod. Although the decomposition solution is also an approximation, one whichdoes not change the problem in a simple form, therefore it is often physically morerealistic. We use mathematica achieve the numerical solutions and realize the process ofcomputer in research and application.