This article is cited in 8 papers

On a problem of the constructive theory of harmonic mappings

S. I. Bezrodnykh^ab, V. I. Vlasov<sup>a

a</sup> Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow, Russia
^b Sternberg Astronomical Institute, Lomonosov Moscow State University, Moscow, Russia

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.

UDC: 517.57

 English version: Journal of Mathematical Sciences, 2014, 201:6, 705–732

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