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Zhurnal SVMO, 2017, Volume 19, Number 3, Pages 41–52 (Mi svmo672)  

Mathematics

Accuracy of difference schemes for nonlinear elliptic equations with non-restricted nonlinearity

F. V. Lubyshev, M. È. Fairuzov, A. R. Manapova

Bashkir State University, Ufa

Abstract: We consider the first boundary-value problem for nonlinear elliptic equations with mixed derivatives and unrestricted nonlinearity. Difference scheme for solution of a given problem class and an iterative process implementing the scheme are constructed and studied. Rigorous study of the iterative processí convergence is conducted. Existence and uniqueness of solution of nonlinear difference scheme approximating the original differential problem are proved. Estimates of convergence rates for difference schemes approximating nonlinear equation with non-restricted nonlinearity are obtained. These estimates are consistent with the smoothness of the sought solution.

Keywords: nonlinear elliptic equations, difference method of solving, accuracy of difference approximations, iterative process

DOI: https://doi.org/10.15507/2079-6900.19.201703.41-52

Full text: PDF file (442 kB)
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UDC: 519.6:517.962
MSC: 65N06

Citation: F. V. Lubyshev, M. È. Fairuzov, A. R. Manapova, “Accuracy of difference schemes for nonlinear elliptic equations with non-restricted nonlinearity”, Zhurnal SVMO, 19:3 (2017), 41–52

Citation in format AMSBIB
\Bibitem{LubFaiMan17}
\by F.~V.~Lubyshev, M.~\`E.~Fairuzov, A.~R.~Manapova
\paper Accuracy of difference schemes for nonlinear elliptic equations with non-restricted nonlinearity
\jour Zhurnal SVMO
\yr 2017
\vol 19
\issue 3
\pages 41--52
\mathnet{http://mi.mathnet.ru/svmo672}
\crossref{https://doi.org/10.15507/2079-6900.19.201703.41-52}
\elib{https://elibrary.ru/item.asp?id=30771193}


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