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

Raimondas Čiegis, Remigijus Čiegis and Ignas Dapšys
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Raimondas Čiegis: Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania
Remigijus Čiegis: Kaunas Faculty, Vilnius University, Muitinės St 8, LT-44280 Kaunas, Lithuania
Ignas Dapšys: Department of Mathematical Modelling, Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania

Mathematics, 2021, vol. 9, issue 12, 1-18

Abstract: 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.

Keywords: fractional power elliptic operators; parabolic equations; nonlinear diffusion-reaction; discrete schemes; splitting methods; stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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