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

Alexander Fedotov
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Alexander Fedotov: N.I.Lobachevskii Institute of Mathematics and Mechanics, Kazan Federal University, Kremliovskaya 35, Kazan 420008, Russian Federation

Mathematics, 2014, vol. 2, issue 1, 1-15

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2014
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