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Mathematics 2014, 2(1), 53-67; doi:10.3390/math2010053

Convergence of the Quadrature-Differences Method for Singular Integro-Differential Equations on the Interval

N.I.Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University, Kremliovskaya 35, Kazan 420008, Russian Federation
Received: 22 December 2013 / Revised: 20 February 2014 / Accepted: 21 February 2014 / Published: 4 March 2014
(This article belongs to the Special Issue Mathematics on Partial Differential Equations)
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Abstract

In this paper, we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with the Cauchy kernel on the interval (–1,1). We consider equations of zero, positive and negative indices. It is shown that the method converges to an exact solution, and the error estimation depends on the sharpness of derivative approximations and on the smoothness of the coefficients and the right-hand side of the equation.
Keywords: singular integro-differential equations; quadrature-differences method singular integro-differential equations; quadrature-differences method
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Fedotov, A. Convergence of the Quadrature-Differences Method for Singular Integro-Differential Equations on the Interval. Mathematics 2014, 2, 53-67.

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