时间分数阶扩散方程的一个新的高阶数值格式
A NEW HIGH ORDER NUMERICAL SCHEME TO THE TIME FRACTIONAL DIFFUSION EQUATIONS
查看参考文献15篇
|
文摘
|
研究时间分数阶扩散方程,利用时间方向的有限差分格式和空间方向的Legendre collocation 谱方法构造了一个高阶稳定格式.一系列的数值试验表明该格式是稳定的,其收敛阶为O(△t~(3-α)+ N~(-m)),这里α, △t,N和m分别为时间分数阶导数的阶数、时间步长、空间多项式逼近阶数和精确解的正则度. |
|
其他语种文摘
|
We investigate the time fractional anomalous diffusion equation on a bounded domain. We propose an efficient method for its numerical solution. This method is based on a finite difference in time and spectral method in space. The numerical examples show the convergence rate is O(△t~(3-α) + N~(-m)), where a, At, N and m are respectively the order of time fractional derivatives, time step size, the polynomial degree and the regularity of the exact solution. |
|
来源
|
数值计算与计算机应用
,2014,35(4):277-288 【扩展库】
|
|
关键词
|
时间分数阶扩散方程
;
高阶数值方法
;
差分法
;
谱方法
|
|
地址
|
贵州民族大学理学院, 贵阳, 550025
|
|
语种
|
中文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
1000-3266 |
|
学科
|
自动化技术、计算机技术 |
|
基金
|
国家自然科学基金
;
贵州省自然科学基金
;
贵州省教育厅
|
|
文献收藏号
|
CSCD:5310348
|
参考文献 共
15
共1页
|
|
1.
Gorenflo R. Random walk models for space-fractional diffusion processes.
Fract. Calc. Appl. Anal,1998,1(2):167-191
|
被引
11
次
|
|
|
|
|
2.
Gorenflo R. Approximation of L'evy-Feller diffusion by random walk.
J. Anal. Appl,1999,18:231-246
|
被引
2
次
|
|
|
|
|
3.
Langlands T. The accuracy and stability of an implicit solution method for the fractional diffusion equation.
J. Comput. Phys,2005,205(2):719-736
|
被引
17
次
|
|
|
|
|
4.
Sun Z Z. A fully discrete difference scheme for a diffusion-wave system.
Appl. Numer. Math,2006,56(2):193-209
|
被引
28
次
|
|
|
|
|
5.
Lin Y M. Finite difference/spectral approximations for the time fractional diffusion equation.
J. Comput. Phys,2007,225(2):1533-1552
|
被引
22
次
|
|
|
|
|
6.
Su L. Finite difference approximations for the fractional advection-diffusion equation.
Phys. Lett. A,2009,373:4405-4408
|
被引
1
次
|
|
|
|
|
7.
Li C. Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion.
Comput. Math. Appl,2011,62:855-875
|
被引
2
次
|
|
|
|
|
8.
Huang J. Two finite difference schemes for time fractional diffusion-wave equation.
Numerical Algorithms,2013,64(4):707-720
|
被引
1
次
|
|
|
|
|
9.
Mohebbi A. Compact finite difference scheme for the solution of time fractional advection-dispersion equation.
Numer. Algor,2013,63(3):431-452
|
被引
1
次
|
|
|
|
|
10.
Ren J. Compact difference scheme for the fractional sub-diffusion equation with Neumann boundary conditions.
J. Comput. Phys,2013,232:456-467
|
被引
2
次
|
|
|
|
|
11.
Lukashchuk S. An approximate solution method for ordinary fractional differential equations with the Riemann-Liouville fractional derivatives.
Commun. Nonlinear Sci. Numer. Simul,2014,19(2):390-400
|
被引
2
次
|
|
|
|
|
12.
Yang J. Numerical solution of fractional diffusion-wave equation based on fractional multistep method.
Appl. Math. Model,2014,38(14):3652-3661
|
被引
2
次
|
|
|
|
|
13.
Gao G. A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications.
J. Comput. Phys,2014,259:33-50
|
被引
6
次
|
|
|
|
|
14.
Podlubny I.
Fractional differential equations,1999
|
被引
723
次
|
|
|
|
|
15.
Xu C. Analysis of iterative methods for the viscous/inviscid coupled problem via a spectral element approximation.
Inter. J. Numer. Meth. Fluids,2000,32(6):619-646
|
被引
1
次
|
|
|
|
|
了解气象卫星更多信息，请访问