Abstract
Charge simulation method (CSM), which is a kind of fundamental solution method, applied to a boundary value problems for Laplace equation in a two-dimensional Jordan region (bounded region whose boundary is a closed Jordan curve) is considered. We prove that if we use an exterior mapping function of the region to determine charge points and collocation points, then CSM solution converges to the exact solution under a hypothesis that the boundary curve is real analytic. We also obtain an error estimate which says that if the boundary data is real analytic, exponential convergence occurs.
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Katsurada, M. Charge simulation method using exterior mapping functions. Japan J. Indust. Appl. Math. 11, 47–61 (1994). https://doi.org/10.1007/BF03167213
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DOI: https://doi.org/10.1007/BF03167213