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

Er Gao*, Songhe Song and Xinjian Zhang

Author Affiliations

Department of Mathematics and Systems Science, College of Science, National University of Defense Technology, Changsha 410073, China

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Boundary Value Problems 2012, 2012:3  doi:10.1186/1687-2770-2012-3

Published: 16 January 2012


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.