A parallel algorithm for space-time-fractional partial differential equations

被引：2

作者：

Lorin, E. ^{[1
,2
]}

机构：

[1] Univ Montreal, Ctr Rech Math, Montreal, PQ, Canada

[2] Carleton Univ, Sch Math & Stat, Ottawa, ON, Canada

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Fractional differential equations; Parallel-in-time algorithm; Pseudospectral method; Approximate solver; DIRAC-EQUATION; PARAREAL; DIFFUSION; APPROXIMATION; EXISTENCE;

D O I：

10.1186/s13662-020-02744-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is dedicated to the derivation of a simple parallel in space and time algorithm for space and time fractional evolution partial differential equations. We report the stability, the order of the method and provide some illustrating numerical experiments.

引用

页数：21

共 40 条

[1] Computational performance of simple and efficient sequential and parallel Dirac equation solvers [J].

Antoine, X. ;

Lorin, E. .

COMPUTER PHYSICS COMMUNICATIONS, 2017, 220 :150-172

[2]

Antoine X., 2019, COUPLING SPECT UNPUB

[3]

Antoine X., 2020, DERIVATION ANA UNPUB

[4] Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces [J].

Antoine, Xavier ;

Fillion-Gourdeau, Francois ;

Lorinc, Emmanuel ;

MacLean, Steve .

JOURNAL OF COMPUTATIONAL PHYSICS, 2020, 411

[5] A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers [J].

Antoine, Xavier ;

Lorin, Emmanuel .

JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 395 :583-601

[6] Towards Perfectly Matched Layers for time-dependent space fractional PDEs [J].

Antoine, Xavier ;

Lorin, Emmanuel .

JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 391 :59-90

[7] High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrodinger/Gross-Pitaevskii equations [J].

Antoine, Xavier ;

Besse, Christophe ;

Rispoli, Vittorio .

JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 327 :252-269

[8]

Bardos C, 2015, NUMER MATH, V129, P749, DOI 10.1007/s00211-014-0652-y

[9] The Parareal in Time Algorithm Applied to the Kinetic Neutron Diffusion Equation [J].

Baudron, A. -M. ;

Lautard, J. -J. ;

Maday, Y. ;

Mula, O. .

DOMAIN DECOMPOSITION METHODS IN SCIENCE AND ENGINEERING XXI, 2014, 98 :437-445

[10] Fractional diffusion in inhomogeneous media [J].

Chechkin, AV ;

Gorenflo, R ;

Sokolov, IM .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2005, 38 (42) :L679-L684

← 1 2 3 4 →