Numerical Application of Adomian Decomposition Method to One Dimensional Wave Equations

Abstract

Adomian decomposition method (ADM) allows us to obtain the exact solution as an infinite series of functions to several classes of equations. It avoids discretization in space and time induced by classical methods of resolution of functional equations. In this paper, we state the general Adomian decomposition method for the wave equation and apply it to problems of one-dimensional wave equations. Four test problems were used to validate the reliability of the method. In all cases, the method gave exact solution in Taylor's series forms, which were the same as the compact analytical exact solution.

Modified New Iterative Method for Solving Nonlinear Partial Differential Equations

“…In this section, the convergence of the series (2), calculated by (18), will be discussed, and it will also be proved that it satisfies the initial value problem (6). But first, the following three lemmas will be presented.…”