The method of approximate particular solutions for solving certain partial differential equations

Abstract

A standard approach for solving linear partial differential equations is to split the solution into a homogeneous solution and a particular solution. Motivated by the method of fundamental solutions for solving homogeneous equations, we propose a similar approach using the method of approximate particular solutions for solving linear inhomogeneous differential equations without the need of finding the homogeneous solution. This leads to a much simpler numerical scheme with similar accuracy to the traditional approach. To demonstrate the simplicity of the new approach, three numerical examples are given with excellent results. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 506–522, 2012