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Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method
Zhang,Lu1; Sun,Hai Wei2
2020-02
Source PublicationJournal of Applied Mathematics and Computing
ISSN1598-5865
Volume62Issue:1-2Pages:449-472
Abstract

A spatial discretization of the Riesz fractional nonlinear reaction–diffusion equation by the fractional centered difference scheme leads to a system of ordinary differential equations, in which the resulting coefficient matrix possesses the symmetric block Toeplitz structure. An exponential Runge–Kutta method is employed to solve such a system of ordinary differential equations. In the practical implementation, the product of a block Toeplitz matrix exponential and a vector is calculated by the shift-invert Lanczos method. Meanwhile, the symmetric positive definiteness of the coefficient matrix guarantees the fast approximation by the shift-invert Lanczos method. Numerical results are given to demonstrate the efficiency of the proposed method.

KeywordExponential Runge–kutta Method Matrix Exponential Riesz Fractional Reaction–diffusion Equation Shift-invert Lanczos Method Toeplitz Structure
DOI10.1007/s12190-019-01291-w
URLView the original
Indexed BySCIE
Language英語English
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000488905000001
PublisherSPRINGER HEIDELBERG, TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
Scopus ID2-s2.0-85074374854
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Cited Times [WOS]:6   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Corresponding AuthorZhang,Lu; Sun,Hai Wei
Affiliation1.School of Mathematics and Physical Sciences Technology,Xuzhou University of Technology,Xuzhou,221018,China
2.Department of Mathematics,University of Macau,Macao
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Zhang,Lu,Sun,Hai Wei. Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method[J]. Journal of Applied Mathematics and Computing,2020,62(1-2):449-472.
APA Zhang,Lu,&Sun,Hai Wei.(2020).Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method.Journal of Applied Mathematics and Computing,62(1-2),449-472.
MLA Zhang,Lu,et al."Numerical solution for multi-dimensional Riesz fractional nonlinear reaction–diffusion equation by exponential Runge–Kutta method".Journal of Applied Mathematics and Computing 62.1-2(2020):449-472.
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