Uniform convergence of the rectangle method for singular integral equation with the Hölder density

M. E. Abramyan

Chair of Algebra and Discrete Mathematics, Southern Federal University, Rostov-on-Don, Russia

Abstract: We investigate an approximate method of solving singular integral equation. The method consists in approximation of singular equation with the use of compound formula of rectangles type. The corresponding systems of linear algebraic equations are uniquely solvable if integral equation is solvable, and coefficients of an equation satisfy the strong ellipticity condition. Under these conditions we estimate the rate of the convergence of solutions of systems of linear equations to the solution of the integral equation in the uniform vector norm.

Keywords: singular integral equation, discretization of integral operators by the method of rectangles, Hölder function, Hölder density, convergence in the uniform vector norm.

UDC: 517.968

Received: 24.02.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:2, 1–9

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