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

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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)

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.

Suggested Citation

  • Raimondas Čiegis & Remigijus Čiegis & Ignas Dapšys, 2021. "A Comparison of Discrete Schemes for Numerical Solution of Parabolic Problems with Fractional Power Elliptic Operators," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1344-:d:572579
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    References listed on IDEAS

    as
    1. El-Nabulsi, Rami Ahmad, 2009. "Fractional Dirac operators and deformed field theory on Clifford algebra," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2614-2622.
    2. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    1. Raimondas Čiegis & Ignas Dapšys, 2022. "On a Framework for the Stability and Convergence Analysis of Discrete Schemes for Nonstationary Nonlocal Problems of Parabolic Type," Mathematics, MDPI, vol. 10(13), pages 1-18, June.

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