Numerical Analysis and Applications

, Volume 12, Issue 1, pp 87–103 | Cite as

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

  • S. B. SorokinEmail author


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.


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


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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