Solving singular second-order initial/boundary value problems in reproducing kernel Hilbert space

In this paper, we presents a reproducing kernel method for computing singular second-order initial/boundary value problems (IBVPs). This method could deal with much more general IBVPs than the ones could do, which are given by the previous researchers. According to our work, in the first step, the a...

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Bibliographic Details
Published inBoundary value problems Vol. 2012; no. 1; pp. 1 - 11
Main Authors Gao, Er, Song, Songhe, Zhang, Xinjian
Format Journal Article
LanguageEnglish
Published New York Hindawi Limited 01.12.2012
Subjects
Approximation
Boundary value problems
Classification
Computation
Construction
Kernels
Mathematical analysis
Mathematical models
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ISSN1687-2762
1687-2770
DOI10.1186/1687-2770-2012-3

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Summary:In this paper, we presents a reproducing kernel method for computing singular second-order initial/boundary value problems (IBVPs). This method could deal with much more general IBVPs than the ones could do, which are given by the previous researchers. According to our work, in the first step, the analytical solution of IBVPs is represented in the RKHS which we constructs. Then, the analytic approximation is exhibited in this RKHS. Finally, the n-term approximation is proved to converge to the analytical solution. Some numerical examples are displayed to demonstrate the validity and applicability of the present method. The results obtained by using the method indicate the method is simple and effective. Mathematics Subject Classification (2000) 35A24, 46E20, 47B32.[PUBLICATION ABSTRACT]
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ISSN:1687-2762
1687-2770
DOI:10.1186/1687-2770-2012-3