Difference schemes for quasi-linear parabolic equations with mixed derivatives
https://doi.org/10.29235/1561-8323-2019-63-3-263-269
Abstract
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 L2.
About the Authors
P. P. Matus
Institute of Mathematics of the National Academy of Sciences of Belarus; Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin
Belarus
Belarus
Matus Petr Pavlovich – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief researcher
11, Surganov Str., 220072, Minsk, Republic of Belarus
Le Minh Hieu
University of Economics, University of Danang
Viet Nam
Viet Nam
Le Minh Hieu – Ph. D. (Physics and Mathematics)
71, Ngu Han Sean Str., 550000, Danang, Vietnam
D. Pylak
Institute of Mathematics and Computer Science The John Paul II Catholic University of Lublin
Poland
Poland
Pylak Dorota – Ph. D. (Physics and Mathematics)
14, Raclawickie Str., 20-950, Lublin, Poland
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