The Method of Approximate Particular Solutions For Solving Certain Partial Differential Equations
Document Type
Article
Publication Date
3-1-2012
Department
Mathematics
School
Mathematics and Natural Sciences
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. (c) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 506522, 2012
Publication Title
Numerical Methods for Partial Differential Equations
Volume
28
Issue
2
First Page
506
Last Page
522
Recommended Citation
Chen, C.,
Fan, C.,
Wen, P.
(2012). The Method of Approximate Particular Solutions For Solving Certain Partial Differential Equations. Numerical Methods for Partial Differential Equations, 28(2), 506-522.
Available at: https://aquila.usm.edu/fac_pubs/241