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An improved non-local boundary value problem method for a cauchy problem of the Laplace equation

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Abstract

In this paper, we propose an improved non-local boundary value problem method to solve a Cauchy problem for the Laplace equation. It is known that the Cauchy problem for the Laplace equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Convergence estimates for the regularized solutions are obtained under a-priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou City, Gansu Province, 730000, People’s Republic of China

    Hongwu Zhang & Ting Wei

  2. Department of Mathematics, Hexi University, Zhangye City, Gansu Province, 734000, People’s Republic of China

    Hongwu Zhang

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  1. Hongwu Zhang
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  2. Ting Wei
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Correspondence to Hongwu Zhang.

Additional information

The work described in this paper was supported by the NSF of China (10971089).

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Zhang, H., Wei, T. An improved non-local boundary value problem method for a cauchy problem of the Laplace equation. Numer Algor 59, 249–269 (2012). https://doi.org/10.1007/s11075-011-9487-0

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