The method of fundamental solution for the inverse source problem for the space-fractional diffusion equation

In this article, a meshless numerical method for solving the inverse source problem of the space-fractional diffusion equation is proposed. The numerical solution is approximated using the fundamental solution of the space-fractional diffusion equation as a basis function. Since the resulting matrix...

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Bibliographic Details
Published in:	Inverse problems in science and engineering Vol. 26; no. 7; pp. 925 - 941
Main Authors:	Wen, Jin, Cheng, Jun-Feng
Format:	Journal Article
Language:	English
Published:	Taylor & Francis 03.07.2018
Subjects:	fractional inverse problem generalized cross-validation inverse source meshless method Method of fundamental solutions
ISSN:	1741-5977, 1741-5985
Online Access:	Get full text
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Summary:	In this article, a meshless numerical method for solving the inverse source problem of the space-fractional diffusion equation is proposed. The numerical solution is approximated using the fundamental solution of the space-fractional diffusion equation as a basis function. Since the resulting matrix equation is extremely ill-conditioned, a regularized solution is obtained by adopting the Tikhonov regularization scheme, in which the choice of the regularization parameter is based on generalized cross-validation criterion. Two typical numerical examples are given to verify the efficiency and accuracy of the proposed method.
ISSN:	1741-5977 1741-5985
DOI:	10.1080/17415977.2017.1369537