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2001•ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und MechanikRequires access

Numerical Computation of a Cauchy Problem for Laplace's Equation

Jin Cheng, Y.C. Hon, Ting Wei, Masahiro Yamamoto

Open publisher page 97 citations

Abstract

This paper investigates the numerical computation of a Cauchy problem for Laplace's equation which is a typical ill-posed problem. By using Green's formula, the problem is transformed to a moment problem. For numerical computation of the moment problem, an error estimation and several numerical examples for verification are presented. Necessary and sufficient conditions for the existence of the solution of the Cauchy problems for Laplace's equation in two-dimension are also given.

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What this paper is about

This paper investigates the numerical computation of a Cauchy problem for Laplace's equation which is a typical ill-posed problem. By using Green's formula, the problem is transformed to a moment problem. For numerical computation of the moment problem, an error estimation and several numerical examples for verification are presented. Necessary and sufficient conditions for the existence of the solution of the Cauchy problems for Laplace's equation in two-dimension are also given.

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OpenAlex reports 97 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper investigates the numerical computation of a Cauchy problem for Laplace's equation which is a typical ill-posed problem. By using Green's formula, the problem is transformed to a moment problem. For numerical computation of the moment problem, an error estimation and several numerical examples for verification are presented. Necessary and sufficient conditions for the existence of the solution of the Cauchy problems for Laplace's equation in two-dimension are also given.

Key concepts: Mathematics, Computation, Cauchy problem, Moment (physics), Laplace's equation, Laplace transform, Green's function for the three-variable Laplace equation, Cauchy distribution

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