Proceedings of A. Razmadze Mathematical Institute (Proc. A. Razmadze Math. Inst.) (20120101), 160, 71-89. ISSN: 1512-0007 (print).
Subject
30 Functions of a complex variable -- 30C Geometric function theory 30C30 Numerical methods in conformal mapping theory
65 Numerical analysis -- 65E Numerical methods in complex analysis 65E05 Numerical methods in complex analysis
65 Numerical analysis -- 65N Partial differential equations, boundary value problems 65N99 None of the above, but in this section
Language
English Georgian
Online Access
초록
Summary: ``In this paper we investigate the question how the method of conformal mapping (MCM) can be applied for approximate solving of the generalized Dirichlet boundary problem for harmonic function. Under the generalized problem is meant the case when a boundary function has a finite number of first kind break points. The problem is considered for finite and infinite simply connected domains. It is shown that the method of fundamental solutions (MFS) is ineffective for solving of the considered problem from the point of view of the accuracy. We propose an efficient algorithm for approximate solving of the generalized problem, which is based on the MCM. Examples of application of the proposed algorithm and the results of numerical experiments are given.''