Uniqueness and convergence of numerical solution of the Cauchy problem for the Laplace equation by a charge simulation method

DOI10.1007/BF03167587zbMath1078.65081MaRDI QIDQ1764350

Kohzaburo Ohnaka, Takashi Ohe

Publication date: 24 February 2005

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

convergenceCauchy problemnumerical experimentsLaplace equationcharge simulation method

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (10)

Asymptotic analysis of the conventional and invariant schemes for the method of fundamental solutions applied to potential problems in doubly-connected regions ⋮ A variational-type method of fundamental solutions for a Cauchy problem of Laplace's equation ⋮ A direct identification method for current dipoles from electromagnetic fields ⋮ Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions ⋮ The MFS for numerical boundary identification in two-dimensional harmonic problems ⋮ FINITE DIFFERENCE APPROXIMATIONS TO THE POISSON EQUATION IN A CLASS OF ANALYTIC FUNCTIONS ⋮ An inverse boundary problem for one-dimensional heat equation with a multilayer domain ⋮ Cauchy problems of Laplace's equation by the methods of fundamental solutions and particular solutions ⋮ A survey of applications of the MFS to inverse problems ⋮ A regularization method for a Cauchy problem of Laplace's equation in an annular domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An iterative method for solving the Cauchy problem for elliptic equations
• Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data
• Partial differential equations. 4th ed
• Comparison of conventional and ``invariant schemes of fundamental solutions method for annular domains
• Numerical solution of a Cauchy problem for the Laplace equation
• Fundamental Solutions Method for Elliptic Boundary Value Problems
• Stable determination of a crack from boundary measurements
• Inverse problems for partial differential equations

This page was built for publication: Uniqueness and convergence of numerical solution of the Cauchy problem for the Laplace equation by a charge simulation method