Open AccessMONOTONE ECONOMICAL SCHEMES FOR QUASILINEAR PARABOLIC EQUATIONS
Author(s) -
N. V. Dzenisenko,
A. P. Matus,
П. П. Матус
Publication year - 2002
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2002.9637193
Subject(s) - mathematics , monotone polygon , equivalence (formal languages) , scheme (mathematics) , a priori and a posteriori , norm (philosophy) , nonlinear system , parabolic partial differential equation , mathematical analysis , pure mathematics , partial differential equation , philosophy , physics , geometry , epistemology , quantum mechanics , political science , law
In order to approximate a multidimensional quasilinear parabolic equation with unlimited nonlinearity the economical vector‐additive scheme is constructed. It is shown that its solution satisfies the maximum principle and, hence, the scheme is monotone. The proof is based on the equivalence of the vector‐additive scheme and the scheme of summarized approximation (locally one‐dimensional scheme). The a priori estimates of the difference solution in the uniform norm are obtained.