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

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 a...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 9; no. 12; p. 1344
Main Authors: Čiegis, Raimondas, Čiegis, Remigijus, Dapšys, Ignas
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.06.2021
Subjects:
Algorithms
Approximation
Boundary conditions
Calculus
discrete schemes
Dynamical systems
Food science
fractional power elliptic operators
Investigations
Methods
nonlinear diffusion-reaction
Operators
parabolic equations
Splitting
splitting methods
stability
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math9121344