This article is cited in 8 papers

Approximate solution of Wiener–Hopf integral equations and its discrete counterparts

A. G. Barseghyan, N. B. Engibaryan

Institute of Mathematics, Academy of Sciences of Armenia, pr. Marshala Baghramyana 24/5, Yerevan, 0019, Armenia

Abstract: A method for averaging the kernel of a numerical-analytical solution of nonsingular Wiener–Hopf (WH) equations is proposed. By applying a discretization technique similar to the strip method, the WH integral equation is reduced to a discrete WH equation. A priori estimates are obtained that ensure the uniform convergence of the method. Two techniques for solving discrete WH equations are developed. The first is based on reducing these equations to finite-diagonal systems with a solution converging in the norm to the solution of the original equation. The second method is based on a modification of the Baxter projection theorem, whereby the strongly converging reduction procedure can be replaced by one converging in the norm.

Key words: nonsingular integral equation, discrete Wiener–Hopf equation, constructive solution, reduction, norm convergence, factorization, projection method.

UDC: 519.642

MSC: Primary 65R20; Secondary 45A05, 45N05

Received: 26.06.2014
Revised: 06.10.2014

DOI: 10.7868/S0044466915050063

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:5, 834–843

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