The method of particular solutions for solving scalar wave equations

A standard approach for solving 2D scalar wave propagation problems is presented with the use of the method of particular solutions (MPS). Motivated by the method of fundamental solutions for solving homogeneous equations, we propose a similar approach using the MPS for solving linear inhomogeneous differential equations without the need of finding the homogeneous solution. The wave equations are analyzed in the Laplace transformed domain and the Durbin inversion method is used to determine the solutions in the time domain. To demonstrate the effectiveness and simplicity of the new approach, three numerical examples have been given with excellent accuracy. Copyright (C) 2009 John Wiley & Sons, Ltd.