A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations

被引：14
作者：
Liu, Jun [1 ]
Zhu, Chen [1 ]
Chen, Yanping [2 ]
Fu, Hongfei [3 ]
机构：
[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China
[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China
[3] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2021年 / 160卷
基金：
中国国家自然科学基金;
关键词：
Space-fractional diffusion equations; ADI; Quadratic spline collocation method; Stability; Convergence; FINITE-DIFFERENCE METHOD; SPECTRAL METHOD; ELEMENT-METHOD; VOLUME METHOD; SCHEME; APPROXIMATIONS; STABILITY; EFFICIENT; CONVERGENCE;
D O I：
10.1016/j.apnum.2020.10.015
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we develop a Crank-Nicolson ADI quadratic spline collocation method for the approximation of two-dimensional two-sided Riemann-Liouville space-fractional diffusion equation, in which a quadratic spline collocation method combined with ADI approach is considered for the discretization of the space-fractional derivatives with orders 1 < alpha, beta < 2, and a Crank-Nicolson method is proposed for the discretization of the first-order time derivative. The novel method is proved to be unconditionally stable for gamma(*) (approximate to 1.2576) < alpha, beta <= 2. Moreover, the method is shown to be convergent with second order in time and min{3 - alpha, 3 - beta} order in space, respectively. Finally, numerical examples are attached to confirm the theoretical results. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：331 / 348
页数：18
相关论文
共 49 条
[1]   The fractional-order governing equation of Levy motion [J].
Benson, DA ;
Wheatcraft, SW ;
Meerschaert, MM .
WATER RESOURCES RESEARCH, 2000, 36 (06) :1413-1423
[2]   Fourier spectral methods for fractional-in-space reaction-diffusion equations [J].
Bueno-Orovio, Alfonso ;
Kay, David ;
Burrage, Kevin .
BIT NUMERICAL MATHEMATICS, 2014, 54 (04) :937-954
[3]   A novel compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations [J].
Cheng, Xiujun ;
Duan, Jinqiao ;
Li, Dongfang .
APPLIED MATHEMATICS AND COMPUTATION, 2019, 346 :452-464
[4]   Variational formulation for the stationary fractional advection dispersion equation [J].
Ervin, VJ ;
Roop, JP .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2006, 22 (03) :558-576
[5]   An ADI Crank-Nicolson Orthogonal Spline Collocation Method for the Two-Dimensional Fractional Diffusion-Wave Equation [J].
Fairweather, Graeme ;
Yang, Xuehua ;
Xu, Da ;
Zhang, Haixiang .
JOURNAL OF SCIENTIFIC COMPUTING, 2015, 65 (03) :1217-1239
[6]   Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation [J].
Feng, L. B. ;
Zhuang, P. ;
Liu, F. ;
Turner, I. .
APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 :52-65
[7]   A finite volume method for two-dimensional Riemann-Liouville space-fractional diffusion equation and its efficient implementation [J].
Fu, Hongfei ;
Liu, Huan ;
Wang, Hong .
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 388 :316-334
[8]   Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equations [J].
Fu, Hongfei ;
Sun, Yanan ;
Wang, Hong ;
Zheng, Xiangcheng .
APPLIED NUMERICAL MATHEMATICS, 2019, 139 :38-51
[9]   POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification [J].
Fu, Hongfei ;
Wang, Hong ;
Wang, Zhu .
JOURNAL OF SCIENTIFIC COMPUTING, 2018, 74 (01) :220-243
[10]   A divide-and-conquer fast finite difference method for space-time fractional partial differential equation [J].
Fu, Hongfei ;
Ng, Michael K. ;
Wang, Hong .
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (06) :1233-1242
12345