Open AccessDifference schemes for quasi-linear parabolic equations with mixed derivatives
Author(s) -
П. П. Матус,
Л. М. Хиеу,
Д. Пылак
Publication year - 2019
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2019-63-3-263-269
Subject(s) - mathematics , monotone polygon , a priori and a posteriori , norm (philosophy) , convergence (economics) , mathematical analysis , differential equation , geometry , philosophy , epistemology , political science , law , economics , economic growth
The present paper is devoted to constructing second-order monotone difference schemes for two-dimensional quasi-linear parabolic equation with mixed derivatives. Two-sided estimates of the solution of specific difference schemes for the original problem are obtained, which are fully consistent with similar estimates of the solution of the differential problem, and the a priori estimate in the uniform norm of C is proved. The estimates obtained are used to prove the convergence of difference schemes in the grid norm of L 2 .