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The method of approximate particular solutions for solving certain partial differential equations. (English) Zbl 1242.65267
Summary: 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.

65N80 Fundamental solutions, Green’s function methods, etc. for boundary value problems involving PDEs
35G05 Linear higher-order PDEs
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