Numerical Application of Adomian Decomposition Method to One Dimensional Wave Equations

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 Taylors series forms, which were the same as the compact analytical exact solution.