Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional

被引：19

作者：

Abdelkawy, M. A. ^{[1
,2
]}

Alyami, S. A. ^{[1
]}

机构：

[1] Imam Mohammad Ibn Saud Islamic Univ, Fac Sci, Dept Math & Stat, Riyadh, Saudi Arabia

[2] Beni Suef Univ, Fac Sci, Dept Math & Comp Sci, Bani Suwayf, Egypt

来源：

CHAOS SOLITONS & FRACTALS | 2021年 / 151卷

关键词：

Collocation method; Shifted Legendre-Gauss-Lobatto quadrature; Shifted Chebyshev Gauss-Radau quadrature; Riesz space-fractional Derivative; COMPACT ADI SCHEME; CONVERGENCE ANALYSIS; NUMERICAL-SOLUTION; GAUSS-COLLOCATION; APPROXIMATION; SIMULATIONS; DIFFERENCE; ALGORITHM; TRANSPORT;

D O I：

10.1016/j.chaos.2021.111279

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A high accurate spectral algorithm for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional (RF-TNRDEs) is consider. We propose a shifted Legendre Gauss-Lobatto collocation (SL GL-C) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the RF-TNRDEs. A complete theoretical formulation is presented and numerical examples are given to illustrate the performance and efficiency of the algorithm. The superiority of the scheme to tackle RFTNRDEs is revealed. (c) 2021 Elsevier Ltd. All rights reserved.

引用

页数：11

共 43 条

[31]

Miller KS, 1993, INTRO FRACTIONAL CAL

[32]

Owolabi K.M., 2019, SPRINGER SERIES COMP, V54

[33] Numerical simulations of chaotic and complex spatiotemporal patterns in fractional reaction-diffusion systems [J].

Owolabi, Kolade M. ;

Atangana, Abdon .

COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (02) :2166-2189

[34]

Podlubny I., 1998, Fractional Differential Equations: An Introduction to fRactional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications

[35] A hybrid method for reactor core simulations employing finite difference and polynomial expansion with improved treatment of transverse leakage [J].

Ray, Sherly ;

Degweker, S. B. ;

Kannan, Umasankari .

ANNALS OF NUCLEAR ENERGY, 2019, 131 :102-111

[36] Fractional kinetic equations: solutions and applications [J].

Saichev, AI ;

Zaslavsky, GM .

CHAOS, 1997, 7 (04) :753-764

[37] Crank-Nicolson difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative [J].

Wang, Dongling ;

Xiao, Aiguo ;

Yang, Wei .

JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 242 :670-681

[38] A finite volume scheme with preconditioned Lanczos method for two-dimensional space-fractional reaction-diffusion equations [J].

Yang, Qianqian ;

Turner, Ian ;

Moroney, Timothy ;

Liu, Fawang .

APPLIED MATHEMATICAL MODELLING, 2014, 38 (15-16) :3755-3762

[39] Finite element method for nonlinear Riesz space fractional diffusion equations on irregular domains [J].

Yang, Z. ;

Yuan, Z. ;

Nie, Y. ;

Wang, J. ;

Zhu, X. ;

Liu, F. .

JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 330 :863-883

[40] Chebyshev collocation treatment of Volterra-Fredholm integral equation with error analysis [J].

Youssri, Y. H. ;

Hafez, R. M. .

ARABIAN JOURNAL OF MATHEMATICS, 2020, 9 (02) :471-480

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