On a Problem of the Constructive Theory of Harmonic Mappings

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 comp...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-09, Vol.201 (6), p.705-732
Main Authors: Bezrodnykh, S. I., Vlasov, V. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-2021-x