Geodesic
Approximate solution of one singular integro-differential equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 35-43

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In this paper we construct and theoretically justify a computational scheme for solving the Cauchy problem for a singular integro-differential equation of the first-order, where the integral over a segment of the real axis is understood in the sense of the Cauchy principal value. In addition, we study and solve approximately the integral equation with a special logarithmic kernel. We obtain uniform estimates for errors of approximate formulas. Orders of errors of approximate solutions are proved to be proportional to the order of the approximation error for the derivative of the density of the singular integral in the integro-differential equation.
Keywords: integro-differential equation, approximate solution, logarithmic kernel, Prandtl equation.
Mots-clés : quadrature formula 
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     author = {I. N. Meleshko and P. G. Lasy},
     title = {Approximate solution of one singular integro-differential equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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     number = {5},
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I. N. Meleshko; P. G. Lasy. Approximate solution of one singular integro-differential equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 35-43. http://geodesic.mathdoc.fr/item/IVM_2011_5_a4/