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.
Apie klasikinio ir apibendrinto hilberto kraštinių uždavinių skaitinių sprendimą
Santrauka. Pateikti du skaitiniai metodai klasikinio ir apibendrinto Hilberto kraštinių uždavinių sprendimui. Pirmasis metodas skirtas klasikinio uždavinio sprendimui, jis remiasi teorema apie atitinkamos integralinės lygties branduolio skleidimą taško τ = t aplinkoje ir Košy tipo integralų skaičiavimo metodais. Apibendrintojo uždavinio sprendimo metodas remiasi metodu, kuris buvo skirtas skaičiuoti singuliarius integralus. Metodai realizuoti Maple ir Mathcad paketais.
Kristalinskii, V. R. (2000). About the approximate solution of the usual and generalized Hilbert boundary value problems for analytical functions. Mathematical Modelling and Analysis, 5(1), 119-126. https://doi.org/10.3846/13926292.2000.9637134
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proposed by the author. All methods are implemented with the Mathcad and Maple.
. Metodai realizuoti Maple ir Mathcad paketais.