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

• Main Author: V. R. Kristalinskii
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2000-12-01
• Series: Mathematical Modelling and Analysis
• Subjects: -
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/9950

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 formproposed by the author. All methods are implemented with the Mathcad and Maple. Apie klasikinio ir apibendrinto hilberto kraštinių uždavinių skaitinių sprendimą Santrauka 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 integralusMetodai realizuoti Maple ir Mathcad paketais. First Published Online: 14 Oct 2010