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The method of approximate particular solutions for solving certain partial differential equations
Author(s) -
Chen C.S.,
Fan C.M.,
Wen P.H.
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20631
Subject(s) - mathematics , homogeneous , numerical partial differential equations , partial differential equation , simplicity , partial derivative , scheme (mathematics) , exponential integrator , method of characteristics , differential equation , homogeneous differential equation , mathematical analysis , differential algebraic equation , ordinary differential equation , philosophy , epistemology , combinatorics
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