An Approximate Solution to the Integral Equations with Kernels of the Form $K(x-t)$ Which Uses a Nonstandard Basis of Trigonometric Functions

V. V. Smelov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: Consider the integral equations with kernels of the form $K(x-t)$. In order to find an approximate solution by the Galerkin method, we propose a nonstandard trigonometric basis. This basis possesses a high approximation quality and enables us to reduce the double integral in the Galerkin algorithm to quite simple single integration.

Keywords: Fredholm and Volterra equations, Galerkin method, nonstandard trigonometric basis.

UDC: 517.968.21+517.968.22

Received: 11.11.2008

 English version: Journal of Applied and Industrial Mathematics, 2010, 4:3, 422–427

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