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

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

Received: 22 December 2013; in revised form: 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

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

AMA Style

Fedotov A. Convergence of the Quadrature-Differences Method for Singular Integro-Differential Equations on the Interval. Mathematics. 2014; 2(1):53-67.

Chicago/Turabian Style

Fedotov, Alexander. 2014. "Convergence of the Quadrature-Differences Method for Singular Integro-Differential Equations on the Interval." Mathematics 2, no. 1: 53-67.

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