Direct Solutions of N-th Order Initial Value Problems in Decomposition Series

摘要

In this paper, a class of linear and non-linear n th-order initial value problems (IVPs) is considered. The solutions of these IVPs are obtained by adapting the modified Adomian decomposition method (MADM) as an algorithm for approximating the solutions of the equations in a sequence of time intervals (i.e. time steps). In this way the series solutions are valid for quite a long time span. Several test cases are chosen to demonstrate the performance of the multistage modified Adomian decomposition method (MMADM).