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

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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 languageEnglish
Pages (from-to)87-103
Number of pages17
JournalNumerical Analysis and Applications
Volume12
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

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

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