Maqola

Compact difference schemes for one-dimensional quasilinear parabolic equations

P. P. MatusInstitute of Mathematics of the National Academy of Sciences of BelarusB. D. UtebaevKarakalpak State University named after Berdakh

Doklady of the National Academy of Sciences of Belarusjournal2026

ABI

Annotatsiya

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.

Mavzular

Differential Equations and Numerical Methods Advanced Numerical Methods in Computational Mathematics Numerical methods for differential equations

Identifikatorlar

DOI: 10.29235/1561-8323-2025-69-6-447-453

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