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On a numerical solution of the Cauchy problem for the Laplace equation by the fundamental solutions method
Author(s) -
Ohe Takashi,
Yamatani Katsu,
Ohnaka Kohzaburo
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700514
Subject(s) - tikhonov regularization , cauchy distribution , mathematics , cauchy problem , regularization (linguistics) , laplace's equation , cauchy's convergence test , domain (mathematical analysis) , mathematical analysis , laplace transform , cauchy boundary condition , initial value problem , method of fundamental solutions , inverse problem , partial differential equation , boundary value problem , computer science , singular boundary method , physics , neumann boundary condition , artificial intelligence , finite element method , boundary element method , thermodynamics
We discuss a numerical method to solve a Cauchy problem for the Laplace equation in the two‐dimensional annular domain. We consider the case that the Cauchy data is given on an arc. We develop an approximation method based of the fundamental solutions method using the least squares method with Tikhonov regularization. The effectiveness of our method is examined by a numerical experiment. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)