Convergence analysis for the Cauchy problem of Laplace’s equation by a regularized method of fundamental solutions

Advances in Computational Mathematics ◽

10.1007/s10444-009-9134-7 ◽

2009 ◽

Vol 33 (4) ◽

pp. 491-510 ◽

Author(s):

T. Wei ◽

D. Y. Zhou

Keyword(s):

Cauchy Problem ◽

Convergence Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

The Cauchy Problem ◽

Regularized Method

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The method of fundamental solutions for solving a Cauchy problem of Laplace's equation in a multi-connected domain

Inverse Problems in Science and Engineering ◽

10.1080/17415970701602614 ◽

2008 ◽

Vol 16 (3) ◽

pp. 389-411 ◽

Author(s):

Dayong Zhou ◽

Ting Wei

Keyword(s):

Cauchy Problem ◽

Connected Domain ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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A variational-type method of fundamental solutions for a Cauchy problem of Laplace’s equation

Applied Mathematical Modelling ◽

10.1016/j.apm.2012.03.023 ◽

2013 ◽

Vol 37 (3) ◽

pp. 1039-1053 ◽

Author(s):

T. Wei ◽

Y.G. Chen ◽

J.C. Liu

Keyword(s):

Cauchy Problem ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Type Method ◽

Laplace's Equation ◽

Variational Type

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Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries

Numerical Algorithms ◽

10.1007/s11075-021-01150-5 ◽

2021 ◽

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Ming-Gong Lee ◽

Hung-Tsai Huang

Keyword(s):

Stability Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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Central difference regularization method for the Cauchy problem of the Laplace’s equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.01.056 ◽

2006 ◽

Vol 181 (1) ◽

pp. 675-684 ◽

Author(s):

Xiang-Tuan Xiong ◽

Chu-Li Fu

Keyword(s):

Cauchy Problem ◽

Regularization Method ◽

Laplace’S Equation ◽

Central Difference ◽

Laplace's Equation ◽

The Cauchy Problem

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Numerical reconstruction of unknown boundary data in the Cauchy problem for Laplace’s equation

Inverse Problems in Science and Engineering ◽

10.1080/17415977.2012.744405 ◽

2013 ◽

Vol 21 (8) ◽

pp. 1255-1267 ◽

Author(s):

Balgaisha Mukanova

Keyword(s):

Cauchy Problem ◽

Boundary Data ◽

Unknown Boundary ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Numerical Reconstruction ◽

The Cauchy Problem

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The cauchy problem for laplace's equation

Siberian Mathematical Journal ◽

10.1007/bf00970903 ◽

1992 ◽

Vol 33 (3) ◽

pp. 534-542 ◽

Author(s):

A. A. Shlapunov

Keyword(s):

Cauchy Problem ◽

Laplace’S Equation ◽

Laplace's Equation ◽

The Cauchy Problem

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Source nodes on elliptic pseudo-boundaries in the method of fundamental solutions for Laplace’s equation; selection of pseudo-boundaries

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2020.112861 ◽

2020 ◽

Vol 377 ◽

pp. 112861 ◽

Author(s):

Fangfang Dou ◽

Li-Ping Zhang ◽

Zi-Cai Li ◽

C.S. Chen

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

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New locations of source nodes for method of fundamental solutions solving Laplace’s equation; pseudo radial-lines

Engineering Analysis with Boundary Elements ◽

10.1016/j.enganabound.2021.12.004 ◽

2022 ◽

Vol 136 ◽

pp. 93-115

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Hung-Tsai Huang ◽

Ming-Gong Lee

Keyword(s):

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

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The Cauchy Problem for Laplace's Equation in Three Dimensions

American Mathematical Monthly ◽

10.1080/00029890.1935.11987678 ◽

1935 ◽

Vol 42 (2) ◽

pp. 65-74

Author(s):

L. H. Johnson

Keyword(s):

Cauchy Problem ◽

Three Dimensions ◽

Laplace’S Equation ◽

Laplace's Equation ◽

The Cauchy Problem

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Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation

Inverse Problems ◽

10.1088/0266-5611/22/2/002 ◽

2006 ◽

Vol 22 (2) ◽

pp. 413-430 ◽

Author(s):

L Bourgeois

Keyword(s):

Cauchy Problem ◽

Convergence Rates ◽

Laplace’S Equation ◽

Laplace's Equation ◽

The Cauchy Problem

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