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December 2015 A Mathematical Analysis of the Complex Dipole Simulation Method
Masashi KATSURADA, Koya SAKAKIBARA
Tokyo J. Math. 38(2): 309-326 (December 2015). DOI: 10.3836/tjm/1452806041

Abstract

We propose the complex dipole simulation method (CDSM) which approximates a holomorphic function by linear combination of $1 / (z - \zeta)$ with the use of its boundary values. In this paper, we treat a function $f$ which is holomorphic in $\Omega$ and continuous on $\overline{\Omega}$ in the case where $\Omega$ is a disk or the exterior domain of a disk. Then we establish the following fact: if $f$ is holomorphic in some neighborhood of $\overline{\Omega}$, the error of an approximate function $f^{(N)}$ decays exponentially with respect to $N$, where $N$ is the number of the charge points.

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Masashi KATSURADA. Koya SAKAKIBARA. "A Mathematical Analysis of the Complex Dipole Simulation Method." Tokyo J. Math. 38 (2) 309 - 326, December 2015. https://doi.org/10.3836/tjm/1452806041

Information

Published: December 2015
First available in Project Euclid: 14 January 2016

zbMATH: 1336.30060
MathSciNet: MR3448858
Digital Object Identifier: 10.3836/tjm/1452806041

Subjects:
Primary: 32A10‎
Secondary: 30E10, 41A20, 65N12, 65N35

Rights: Copyright © 2015 Publication Committee for the Tokyo Journal of Mathematics

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Vol.38 • No. 2 • December 2015
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