The numerical solution of multidimensional partial differential equations by the decomposition method

Abstract

The Adomian decomposition method is used to implement the nonhomogeneous multidimensional partial differential equation model problem. The analytic solution of the equation is calculated in the form of a series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling noise terms whose sum vanishes in the limit. Comparing the methodology with some known techniques shows that the present approach is effective and powerful. Two test problems of Mathematical Physics, are discussed to illustrate the effectiveness and the performance of the decomposition method.