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

被引：10

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

页码：331 / 348

页数：18

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