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Journal of Mathematical Sciences

, Volume 201, Issue 6, pp 705–732 | Cite as

On a Problem of the Constructive Theory of Harmonic Mappings

  • S. I. Bezrodnykh
  • V. I. Vlasov
Article

Abstract

The problem of irremovable error appears in finite difference realization of the Winslow approach in the constructive theory of harmonic mappings. As an example, we consider the well-known Roache–Steinberg problem and demonstrate a new approach, which allows us to construct harmonic mappings of complicated domains effectively and with high precision. This possibility is given by the analytic-numerical method of multipoles with exponential convergence rate. It guarantees effective construction of a harmonic mapping with precision controlled by an a posteriori estimate in a uniform norm with respect to the domain.

Keywords

Dirichlet Problem Conformal Mapping Constructive Theory Grid Generation Harmonic Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. 1.Dorodnitsyn Computing Center of the Russian Academy of SciencesMoscowRussia
  2. 2.Sternberg Astronomical Institute of the Lomonosov Moscow State UniversityMoscowRussia

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