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Sibirskii Zhurnal Industrial'noi Matematiki, 2009, Volume 12, Number 3, Pages 110–116 (Mi sjim572)  
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
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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.
Received: 11.11.2008
English version:
Journal of Applied and Industrial Mathematics, 2010, Volume 4, Issue 3, Pages 422–427
DOI: https://doi.org/10.1134/S1990478910030142
Bibliographic databases:
UDC: 517.968.21+517.968.22
Language: Russian
Citation: 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”, Sib. Zh. Ind. Mat., 12:3 (2009), 110–116; J. Appl. Industr. Math., 4:3 (2010), 422–427
Citation in format AMSBIB
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\by V.~V.~Smelov
\paper An Approximate Solution to the Integral Equations with Kernels of the Form $K(x-t)$ Which Uses a~Nonstandard Basis of Trigonometric Functions
\jour Sib. Zh. Ind. Mat.
\yr 2009
\vol 12
\issue 3
\pages 110--116
\mathnet{http://mi.mathnet.ru/sjim572}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2668790}
\transl
\jour J. Appl. Industr. Math.
\yr 2010
\vol 4
\issue 3
\pages 422--427
\crossref{https://doi.org/10.1134/S1990478910030142}
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