TY - JOUR

T1 - An Efficient Direct Method for Numerically Solving the Cauchy Problem for Laplace’s Equation

AU - Sorokin, S. B.

N1 - Publisher Copyright: © 2019, Pleiades Publishing, Ltd.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - Cauchy problem for Laplace’s equation

KW - efficient direct method

KW - inverse problem

KW - numerical solution

UR - http://www.scopus.com/inward/record.url?scp=85064057668&partnerID=8YFLogxK

U2 - 10.1134/S1995423919010075

DO - 10.1134/S1995423919010075

M3 - Article

AN - SCOPUS:85064057668

VL - 12

SP - 87

EP - 103

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -