Compact difference schemes for one-dimensional quasilinear parabolic equations
https://doi.org/10.29235/1561-8323-2025-69-6-447-453
Abstract
Compact finite difference schemes of approximation orders 4 + 1 and 4 + 2, constructed on minimal stencils, are presented and investigated for the one-dimensional non-stationary quasilinear heat equation, and do not require an iterative process for their implementation. The computational efficiency is achieved by parallelizing the Thomas algorithm over even and odd grid nodes. The monotonicity conditions are obtained and two-sided estimates of the difference solution and a priori estimates in the uniform norm are proved. Computational experiments are also presented to illustrate the effectiveness of the proposed methods, as well as their convergence with the corresponding order.
Keywords
Supporting agencies: The work of the first author was supported by the Belarusian Republican Foundation for Fundamental Research (project no. F25UZB-008), and the work of the second author was supported by the Ministry of Higher Education, Science and Innovation of the Republic of Uzbekistan (project no. FL-8824063232).
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
11, Surganov Str., 220072, Minsk
B. D. Utebaev
Karakalpak State University named after Berdakh
Uzbekistan
Uzbekistan
Utebaev Bakhadir D. – Ph. D. (Physics and Mathematics), Associate Professor
1, Ch. Abdirov Str., 230112, Nukus
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