A CRANK-NICOLSON ADI SPECTRAL METHOD FOR A TWO-DIMENSIONAL RIESZ SPACE FRACTIONAL NONLINEAR REACTION-DIFFUSION EQUATION

被引：308

作者：

Zeng, Fanhai ^{[1
,2
]}

Liu, Fawang ^{[3
]}

Li, Changpin ^{[1
]}

Burrage, Kevin ^{[3
,4
]}

Turner, Ian ^{[3
]}

Anh, V. ^{[3
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[3] Queensland Univ Technol, Sch Math Sci, Brisbane, Qld 4001, Australia

[4] Univ Oxford, OCISB, Dept Comp Sci, Oxford OXI 3QD, England

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2014年 / 52卷 / 06期

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

alternating direction implicit method; Legendre spectral method; Riesz space fractional reaction-diffusion equation; fractional FitzHugh-Nagumo model; stability and convergence; FINITE-DIFFERENCE METHOD; GALERKIN METHOD; NUMERICAL APPROXIMATION; ANOMALOUS DIFFUSION; SUBDIFFUSION; CONVERGENCE; STABILITY;

D O I：

10.1137/130934192

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new alternating direction implicit Galerkin-Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank-Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order 2 in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh-Nagumo model. Numerical results are provided to verify the theoretical analysis.

引用

页码：2599 / 2622

页数：24

共 50 条

[1] Linearized Crank-Nicolson Scheme for the Two-Dimensional Nonlinear Riesz Space-Fractional Convection-Diffusion Equation
Basha, Merfat
Anley, Eyaya Fekadie
Dai, Binxiang
[J]. FRACTAL AND FRACTIONAL, 2023, 7 (03)
[2] A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
Zhang, Hui
Liu, Fawang
Jiang, Xiaoyun
Zeng, Fanhai
Turner, Ian
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 76 (10) : 2460 - 2476
[3] Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
Celik, Cem
Duman, Melda
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (04) : 1743 - 1750
[4] An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation
Fairweather, Graeme
Yang, Xuehua
Xu, Da
Zhang, Haixiang
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2015, 65 (03) : 1217 - 1239
[5] A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equation
Hu, Dongdong
Cao, Xuenian
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2020, 97 (09) : 1928 - 1948
[6] An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems
Fernandes, Ryan I.
Fairweather, Graeme
[J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (19) : 6248 - 6267
[7] Compact ADI Method for Two-Dimensional Riesz Space Fractional Diffusion Equation
Valizadeh, Sohrab
Malek, Alaeddin
Borhanifara, Abdollah
[J]. FILOMAT, 2021, 35 (05) : 1543 - 1554
[8] A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations
Cheng, Xiujun
Duan, Jinqiao
Li, Dongfang
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 346 : 452 - 464
[9] A compact ADI Crank-Nicolson difference scheme for the two-dimensional time fractional subdiffusion equation
Li, Mingzhu
Ma, Qiang
Ding, Xiaohua
[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2018, 95 (12) : 2525 - 2538
[10] Legendre-Chebyshev spectral collocation method for two-dimensional nonlinear reaction-diffusion equation with Riesz space-fractional
Abdelkawy, M. A.
Alyami, S. A.
[J]. CHAOS SOLITONS & FRACTALS, 2021, 151

← 1 2 3 4 5 →