About the approximate solution of the usual and generalized Hilbert boundary value problems for analytical functions

Abstract

In this article the methods for obtaining the approximate solution of usual and generalized Hilbert boundary value problems are proposed. The method of solution of usual Hilbert boundary value problem is based on the theorem about the representation of the kernel of the corresponding integral equation by τ = t and on the earlier proposed method for the computation of the Cauchy‐type integrals. The method for approximate solution of the generalized boundary value problem is based on the method for computation of singular integral of the form

proposed by the author. All methods are implemented with the Mathcad and Maple.

Pateikti du skaitiniai metodai klasikinio ir apibendrinto Hilberto kraštiniu uždaviniu sprendimui. Pirmasis metodas skirtas klasikinio uždavinio sprendimui, jis remiasi teorema apie atitinkamos integralines lygties branduolio skleidima taško τ = t aplinkoje ir Košy tipo integralu skaičiavimo metodais. Apibendrintojo uždavinio sprendimo metodas remiasi metodu, kuris buvo skirtas skaičiuoti singuliarius integralus

Metodai realizuoti Maple ir Mathcad paketais.