Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions

DOI10.1016/j.enganabound.2013.01.017zbMath1297.65137OpenAlexW2099397409MaRDI QIDQ463687

John Y. Chiang, Li-Ping Zhang, Yi-Min Wei, Zi Cai Li

Publication date: 17 October 2014

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2013.01.017

zbMATH Keywords

Dirichlet problemstability analysisregularizationerror analysisCauchy problemsmethod of fundamental solutionsmethod of particular solutionsboundary noise

Mathematics Subject Classification ID

Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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The method of fundamental solutions for the Helmholtz equation ⋮ Neumann problems of 2D Laplace's equation by method of fundamental solutions ⋮ Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions ⋮ Regularization method for an ill-posed Cauchy problem for elliptic equations ⋮ On numerical solution stability of the Laplace equation in absence of the Dirichlet boundary condition: benchmark problem proposal ⋮ Analysis of the dipole simulation method for two-dimensional Dirichlet problems in Jordan regions with analytic boundaries

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