A Regularization Method for the Approximate Particular Solution of Nonhomogeneous Cauchy Problems of Elliptic Partial Differential Equations with Variable Coefficients

Document Type

Article

Publication Date

3-1-2012

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

Radial basis functions (RBFs) have proved to be very flexible in representing functions. Based on the idea of the analog equation method and radial basis functions, in this paper, ill-posed Cauchy problems of elliptic partial differential equations (PDEs) with variable coefficients are considered for the first time using the method of approximate particular solutions (MAPS). We show that, using the Tikhonov regularization. the MAPS results an effective and accurate numerical algorithm for elliptic PDEs and irregular solution domains. Comparing the proposed MAPS with Kansa's method, numerical results show that the proposed MAPS is effective, accurate and stable to solve the ill-posed Cauchy problems. (C) 2011 Elsevier Ltd. All rights reserved.

Publication Title

Engineering Analysis with Boundary Elements

Volume

36

Issue

3

First Page

274

Last Page

280

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