[1]马亮亮,谭千蓉,刘冬兵.非线性变阶空间-时间分数阶对流-扩散方程的全隐式有限差分格式[J].四川师范大学学报(自然科学版),2018,(05):627-634.[doi:10.3969/j.issn.1001-8395.2018.05.010]
 MA Liangliang,TAN Qianrong,LIU Dongbing.Fully Implicit Finite Difference Scheme for the Nonlinear Variable-Order Space-Time Fractional Advection-Diffusion Equation[J].Journal of SichuanNormal University,2018,(05):627-634.[doi:10.3969/j.issn.1001-8395.2018.05.010]
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非线性变阶空间-时间分数阶对流-扩散方程的全隐式有限差分格式()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年05期
页码:
627-634
栏目:
基础理论
出版日期:
2018-06-15

文章信息/Info

Title:
Fully Implicit Finite Difference Scheme for the Nonlinear Variable-Order Space-Time Fractional Advection-Diffusion Equation
文章编号:
1001-8395(2018)05-0627-08
作者:
马亮亮 谭千蓉 刘冬兵
攀枝花学院 数学与计算机学院, 四川 攀枝花 617000
Author(s):
MA Liangliang TAN Qianrong LIU Dongbing
College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, Sichuan
关键词:
变阶空间-时间分数阶对流-扩散方程 全隐式有限差分格式 收敛性 稳定性 能量方法
Keywords:
variable-order fractional advection-diffusion equation fully implicit finite difference scheme convergence stability energy method
分类号:
O241.82
DOI:
10.3969/j.issn.1001-8395.2018.05.010
文献标志码:
A
摘要:
针对非线性变阶空间-时间分数阶对流-扩散方程的初边值问题,提出一种全隐式有限差分格式.首先,分别对Riemann-Liouville型变时间分数阶导数算子和Riemann-Liouville 型变空间分数阶导数算子和广义Riesz分数阶导数算子进行离散化处理; 然后,通过离散的能量方法证明全隐式有限差分格式的稳定性和收敛性,并验证其收敛阶为O(τ+h); 最后,通过数值算例检验该方法.试验结果表明:全隐式有限差分格式求解非线性变阶空间-时间分数阶对流-扩散方程初边值问题是可行和有效的.
Abstract:
A fully implicit finite difference scheme for the nonlinear variable-order fractional advection-diffusion equation was considered.Firstly, the Riemann-Liouville variable order time fractional derivative, the Riemann-Liouville variable order space fractional derivative and the generalized Riesz fractional derivative were discretized respectively.Then, the convergence and the stability of the fully implicit finite difference scheme were obtained by discrete energy method, and the convergence order of the scheme was inally, a numerical example was provided to test this method.The results demonstrated the feasibility and the efficiency of the proposed method.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2017-03-03 接受日期:2017-04-25
基金项目:国家自然科学基金(10671132和60673192)、四川省教育厅自然科学基金(16ZA0411)、四川省科技厅资助项目(2013JY0125)和攀枝花市自然科学基金(2014CY-G-22)
第一作者简介:马亮亮(1986—),男,讲师,主要从事模型优化和微分方程的研究,E-mail:mllpzh@126.com
更新日期/Last Update: 2018-04-15