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On convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson’s equation

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Abstract

In this paper the convergence of using the method of fundamental solutions for solving the boundary value problem of Laplace’s equation in R2 is established, where the boundaries of the domain and fictitious domain are assumed to be concentric circles. Fourier series is then used to find the particular solutions of Poisson’s equation, which the derivatives of particular solutions are estimated under the L 2 norm. The convergent order of solving the Dirichlet problem of Poisson’s equation by the method of particular solution and method of fundamental solution is derived.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV, 89154-4020, USA

    Xin Li

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  1. Xin Li
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Correspondence to Xin Li.

Additional information

Communicated by B.Y. Guo

Dedicated to Charles A. Micchelli with esteem on the occasion of his 60th birthday

AMS subject classification

35J05, 31A99

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Li, X. On convergence of the method of fundamental solutions for solving the Dirichlet problem of Poisson’s equation. Adv Comput Math 23, 265–277 (2005). https://doi.org/10.1007/s10444-004-1782-z

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  • DOI: https://doi.org/10.1007/s10444-004-1782-z

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