CONSTRUCTION OF A HIGH-PRECISION APPROXIMATE SOLUTION INTEGRAL WIENER-HOPF EQUATION ON THE SEGMENT

A new rather simple and, at the same time, high-precision method for solving Wiener-Hopf integral equations on a finite segment is proposed. Previously, when solving these equations, it was not possible to construct a single solution that is valid for all segment sizes. Various asymptotic and approximate methods have been constructed for large and small relative segments, which complicates the efficiency of the study. In this paper, on the basis of projection and factorization methods, including those developed by the authors, an approach is proposed that allows constructing a single solution for all relative sizes of the segment of the integral equation assignment. The type of properties of the kernels of integral equations for which this method is applicable is indicated in the article.

Wiener-Hopf integral equation, fictitious absorption method, projection method