A NOTE ON THE APPROXIMATION OF PDES WITH UNBOUNDED COEFFICIENTS -- THE SPECIAL ONE-DIMENSIONAL CASE

Autor:	M.R. Grossinho, F.F. Gon c{c}alves, Eduardo Souza de Morais
Rok vydání:	2020
Předmět:	Non-divergent Operators Computational Theory and Mathematics Finite-difference Methods Unbounded Coefficients General Mathematics Parabolic PDEs Cauchy Problem Weighted Sobolev Spaces Mathematics
Zdroj:	International Journal of Apllied Mathematics. 33
ISSN:	1314-8060 1311-1728
DOI:	10.12732/ijam.v33i1.11
Popis:	We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case. info:eu-repo/semantics/publishedVersion
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cfabd833eb7e258c72a8c745b4b637dd https://doi.org/10.12732/ijam.v33i1.11 Zobrazit plný text záznamu