On a problem of the constructive theory of harmonic mappingsстатья
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Дата последнего поиска статьи во внешних источниках: 28 мая 2015 г.
Аннотация: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.