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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.

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