期刊
APPLIED NUMERICAL MATHEMATICS
卷 119, 期 -, 页码 126-145出版社
ELSEVIER
DOI: 10.1016/j.apnum.2017.04.004
关键词
Stability analysis; Error analysis; Condition number; Method of fundamental solutions; Neumann problems; Truncated singular value decomposition
资金
- Ministry of Science and Technology, Taiwan [MOST 103-2632-M-214-001-MY3]
The method of fundamental solutions (MFS) was first used by Kupradze in 1963 [21]. Since then, there have appeared numerous reports of the MFS. Most of the existing analysis for the MFS are confined to Dirichlet problems on disk domains. It seems to exist no analysis for Neumann problems. This paper is devoted to Neumann problems in non-disk domains, and the new stability analysis and the error analysis are made. The bounds for both condition numbers and errors are derived in detail. The optimal convergence rates in L-2 and H-1 norms in S are achieved, and the condition number grows exponentially as the number of fundamental functions increases. To reduce the huge condition numbers, the truncated singular value decomposition (TSVD) may be solicited. Numerical experiments are provided to support the analysis made. The analysis for Neumann problems in this paper is intriguing due to its distinct features. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
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