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Convergence analysis for the Cauchy problem of Laplace’s equation by a regularized method of fundamental solutions

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Abstract

In this paper, we consider the Cauchy problem of Laplace’s equation in the neighborhood of a circle. The method of fundamental solutions (MFS) combined with the discrete Tikhonov regularization is applied to obtain a regularized solution from noisy Cauchy data. Under the suitable choices of a regularization parameter and an a priori assumption to the Cauchy data, we obtain a convergence result for the regularized solution. Numerical experiments are presented to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, People’s Republic of China

    T. Wei & D. Y. Zhou

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  1. T. Wei
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  2. D. Y. Zhou
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Correspondence to T. Wei.

Additional information

Communicated by the guest editors Benny Hon, Jin Cheng and Masahiro Yamamoto.

The work described in this paper was supported by the NSF of China (10571079, 10671085) and the program of NCET.

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Wei, T., Zhou, D.Y. Convergence analysis for the Cauchy problem of Laplace’s equation by a regularized method of fundamental solutions. Adv Comput Math 33, 491–510 (2010). https://doi.org/10.1007/s10444-009-9134-7

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  • DOI: https://doi.org/10.1007/s10444-009-9134-7

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