A computational approach to the wave equations - An application of the decomposition method

Abstract

Studies an analytic solution and a reliable numerical approximation of linear and non-linear wave equations by using the Adomian decomposition method. The solution is calculated in the form of a series with easily computable components. The non-homogeneous problem is quickly solved by observing the self-cancelling noise terms where the sum of the components vanishes in the limit. Several linear or non-linear partial differential equations are considered and their numerical approximate solutions are compared with its numerical analytic solutions by applying the Adomian decomposition method and using a computer algebraic system (MATLAB). The numerical results show the effectiveness of the method for these types of equations.