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Numerical Algorithms
Erschienen in: Numerical Algorithms 1/2024

07.06.2023 | Original Paper

A fast and high-order IMEX method for non-linear time-space-fractional reaction-diffusion equations

verfasst von: Kamran Kazmi

Erschienen in: Numerical Algorithms | Ausgabe 1/2024

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Abstract

An efficient and high-order numerical method is presented for solving a time-space-fractional reaction-diffusion equation. Matrix transfer technique based on fourth-order compact finite differences is first used to discretize the space-fractional Laplacian operator which results in a system with a linear stiff term. Then, an implicit-explicit (IMEX) trapezoidal product-integration rule is implemented for time integration which treats the stiff linear term implicitly and non-linear non-stiff term explicitly. The stability and convergence of the method are analyzed. Due to the discontinuity of the solution derivative at \(t=0\), the numerical method is only \(1+\alpha \) order accurate in time where \(\alpha \) is the order of the time-fractional derivative. Richardson extrapolation is introduced to obtain a modified version of the method which is second order accurate in time. A fast algorithm based on discrete sine transform is also implemented to reduce the cost of computing the discretized space-fractional Laplacian operator.
Vorheriger Artikel A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems
Nächster Artikel A complex structure-preserving algorithm for computing the singular value decomposition of a quaternion matrix and its applications

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Metadaten
Titel
A fast and high-order IMEX method for non-linear time-space-fractional reaction-diffusion equations
verfasst von
Kamran Kazmi
Publikationsdatum
07.06.2023
Verlag
Springer US
Erschienen in
Numerical Algorithms / Ausgabe 1/2024
Print ISSN: 1017-1398
Elektronische ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-023-01570-5

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