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A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators

1
Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
2
Kaunas Faculty, Vilnius University, Muitinės St 8, LT-44280 Kaunas, Lithuania
*
Author to whom correspondence should be addressed.
Academic Editor: Giancarlo Consolo
Mathematics 2021, 9(12), 1344; https://doi.org/10.3390/math9121344
Received: 12 May 2021 / Revised: 4 June 2021 / Accepted: 8 June 2021 / Published: 10 June 2021
(This article belongs to the Section Computational and Applied Mathematics)
The main aim of this article is to analyze the efficiency of general solvers for parabolic problems with fractional power elliptic operators. Such discrete schemes can be used in the cases of non-constant elliptic operators, non-uniform space meshes and general space domains. The stability results are proved for all algorithms and the accuracy of obtained approximations is estimated by solving well-known test problems. A modification of the second order splitting scheme is presented, it combines the splitting method to solve locally the nonlinear subproblem and the AAA algorithm to solve the nonlocal diffusion subproblem. Results of computational experiments are presented and analyzed. View Full-Text
Keywords: fractional power elliptic operators; parabolic equations; nonlinear diffusion-reaction; discrete schemes; splitting methods; stability fractional power elliptic operators; parabolic equations; nonlinear diffusion-reaction; discrete schemes; splitting methods; stability
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MDPI and ACS Style

Čiegis, R.; Čiegis, R.; Dapšys, I. A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators. Mathematics 2021, 9, 1344. https://doi.org/10.3390/math9121344

AMA Style

Čiegis R, Čiegis R, Dapšys I. A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators. Mathematics. 2021; 9(12):1344. https://doi.org/10.3390/math9121344

Chicago/Turabian Style

Čiegis, Raimondas; Čiegis, Remigijus; Dapšys, Ignas. 2021. "A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators" Mathematics 9, no. 12: 1344. https://doi.org/10.3390/math9121344

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