Monotone difference schemes of higher accuracy for parabolic equations
https://doi.org/10.29235/1561-8323-2020-64-4-391-398
Abstract
In this article, monotone difference schemes for linear inhomogeneous parabolic equations, the Fisher or Kolmogorov-Petrovsky-Piskunov equations are constructed and investigated. The stability and convergence of the proposed methods in the uniform norm L∞ or С is proved. The results obtained are generalized to arbitrary semi-linear parabolic equations with an arbitrary nonlinear sink, as well as to quasi-linear equations.
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 Piotr P. - Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief researcher. Institute of Mathematics of the National Academy of Sciences of Belarus.
11, Surganov Str., 220072, Minsk.
B. D. Utebaev
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Utebaev Bakhadir D. - Postgraduate student. Institute of Mathematics of the National Academy of Sciences of Belarus.
11, Surganov Str., 220072, Minsk.
References
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