An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace’s Equation

S. B. Sorokin

doi:10.1134/S1995423919010075

An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace’s Equation

S. B. Sorokin

Computational Mathematics Section

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A widespread approach to solving the Cauchy problem for Laplace’s equation is to reduce it to an inverse problem. As a rule, an iterative procedure is used to solve this problem. In this study, an efficient direct method for numerically solving the inverse problem in rectangular domains is described. The main idea is to expand the desired solution with respect to a basis consisting of eigenfunctions of a difference analogue of Laplace’s operator.

Original language	English
Pages (from-to)	87-103
Number of pages	17
Journal	Numerical Analysis and Applications
Volume	12
Issue number	1
DOIs	https://doi.org/10.1134/S1995423919010075
Publication status	Published - 1 Jan 2019

Keywords

Cauchy problem for Laplace’s equation
efficient direct method
inverse problem
numerical solution

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10.1134/S1995423919010075

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