Cubature-Differences Method for Singular Integro-differential Equations

Alexander I. Fedotov ()
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Alexander I. Fedotov: Chebotarev Institute of Mathematics & Mechanics

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 308-315 from Springer

Abstract: Summary In the papers [1] - [4] the quadrature-differences methods for the various classes of the 1-dimensional periodic singular integro-differential equations with Hilbert kernels were justified. The convergence of the methods was proved and error estimates were obtained. Here we propose and justify the cubature-differences method for 2-dimensional 1 linear periodic singular integro-differential equations. Such equations appear in the theory of elastity (see [5]) and in some problems of diffraction of electromagnetic waves (see e.g. [6]) The convergence of the method is proved and error estimate is obtained.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_28

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DOI: 10.1007/978-3-642-18775-9_28

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