An efficient direct method for the numerical solution to the Cauchy problem for the Laplace equation
S.B. Sorokin1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Akad. Lavrentjeva 6, Novosibirsk, 630090
2Novosibirsk State University, st. Pirogova 2, Novosibirsk, 630090
Keywords: задача Коши для уравнения Лапласа, обратная задача, численное решение, экономичный прямой метод, Cauchy problem for Laplace equation, inverse problem, numerical solution, efficient direct method
Abstract
One of widespread approaches to solving the Cauchy problem for the Laplace equation is to reduce it to the inverse problem. As a rule, an iterative procedure to solve the latter is used. In this study, an efficient direct method for the numerical solution of the inverse problem in the rectangular form is described. The main idea is based on the expansion of the desired solution with respect to a basis consisting of eigenfunctions of a difference analogue of the Laplace operator.
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