Geodesic
An Approximate Solution to the Integral Equations with Kernels of the Form $K(x-t)$ Which Uses a~Nonstandard Basis of Trigonometric Functions
Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 110-116

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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. 
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V. V. Smelov. An Approximate Solution to the Integral Equations with Kernels of the Form $K(x-t)$ Which Uses a~Nonstandard Basis of Trigonometric Functions. Sibirskij žurnal industrialʹnoj matematiki, Tome 12 (2009) no. 3, pp. 110-116. http://geodesic.mathdoc.fr/item/SJIM_2009_12_3_a10/