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An accuracy of difference schemes for nonlinear elliptic equations with unbounded nonlinearity

TitleAn accuracy of difference schemes for nonlinear elliptic equations with unbounded nonlinearity
AuthorsF. V. Lubyshev1, M. E. Fairuzov1, A. R. Manapova1
1Bashkir State University
AnnotationWe consider the first boundary value problem for nonlinear elliptic equations with mixed derivatives and unrestricted nonlinearity. Is constructed and studied difference scheme for solution of a given problem class and implements its iterative process. Conducted a rigorous study of the convergence of the iterative process, by which is proved the existence and uniqueness of solutions of nonlinear difference scheme approximating the original differential problem. Installed consistent with the smoothness of the sought solution evaluation of the rate of convergence of difference schemes in the mesh norm of $W_{2,0}^2(\omega)$ approximating a nonlinear equation with unbounded nonlinearity.
Keywordsnonlinear elliptic equations, difference method of solving, accuracy, difference approximations, iterative process
CitationLubyshev F. V., Fairuzov M. E., Manapova A. R. ''An accuracy of difference schemes for nonlinear elliptic equations with unbounded nonlinearity'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 115-118. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper17.pdf. - Date of access: 24.08.2019.