Solution of Cauchy Problems by the Multiple Scale Method of Particular Solutions Using Polynomial Basis Functions
Year: 2018
Communications in Computational Physics, Vol. 24 (2018), Iss. 5 : pp. 1409–1434
Abstract
We have recently proposed a new meshless method for solving second order partial differential equations where the polynomial particular solutions are obtained analytically [1]. In this paper, we further extend this new method for the solution of general two- and three-dimensional Cauchy problems. The resulting system of linear equations is ill-conditioned, and therefore, the solution will be regularized by using a multiple scale technique in conjunction with the Tikhonov regularization method, while the L-curve approach is used for the determination of a suitable regularization parameter. Numerical examples including 2D and 3D problems in both smooth and piecewise smooth geometries are given to demonstrate the validity and applicability of the new approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0187
Communications in Computational Physics, Vol. 24 (2018), Iss. 5 : pp. 1409–1434
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Method of particular solution polynomial basis function multiple scale technique regularization technique Cauchy problem.
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