Monotone difference schemes for quasilinear parabolic equations with reaction coefficients of arbitrary sign
https://doi.org/10.29235/1561-8323-2026-70-3-183-190
Abstract
This paper establishes continuous and discrete two-sided estimates for a class of quasilinear parabolic convection–diffusion–reaction equations with unbounded nonlinearities and reaction coefficients of arbitrary sign. For nonpositive reaction coefficients, rigorous continuous two-sided bounds are derived for classical solutions, together with an a priori estimate in the strong C-norm. These results extend, in a structurally coherent manner, the corresponding theory available for linear parabolic problems. For reaction coefficients of arbitrary sign, second-order unconditionally monotone schemes are constructed. By applying the Ladyzhenskaya transformation u = veλt, alternative discrete two-sided estimates are derived for the numerical solution and shown to be fully consistent with their continuous counterparts. Finally, convergence of the developed schemes is rigorously proved in the L2-norm.
About the Authors
P. P. Matus
Institute of Mathematics of the National Academy of Sciences of Belarus
Belarus
Belarus
Matus Piotr P. – Corresponding Member, D. Sc. (Physics and Mathematics), Professor, Chief Researcher
Minsk
Hieu Le Minh
University of Economics, The University of Danang
Viet Nam
Viet Nam
Le Minh Hieu – Ph. D. (Physics and Mathematics), Lecturer, Researcher
71, Ngu Hanh Son Str., 50000, Da Nang
A. L. Gladkov
Belarusian State University
Belarus
Belarus
Gladkov Alexander L. – D. Sc. (Physics and Mathem atics), Professor, Head of the Department
Minsk
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