IMPROVED ERROR ESTIMATES OF A FINITE DIFFERENCE/SPECTRAL METHOD FOR TIME-FRACTIONAL DIFFUSION EQUATIONS

被引:1
|
作者
Lv, Chunwan
Xu, Chuanju [1 ]
机构
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
关键词
Error estimates; finite difference methods; spectral methods; time fractional diffusion equation; DISPERSION; TRANSPORT;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we first consider the numerical method that Lin and Xu proposed and analyzed in [Finite difference/spectral approximations for the time-fractional diffusion equation, JCP 2007] for the time-fractional diffusion equation. It is a method basing on the combination of a finite different scheme in time and spectral method in space. The numerical analysis carried out in that paper showed that the scheme is of (2 - alpha)-order convergence in time and spectral accuracy in space for smooth solutions, where alpha is the time-fractional derivative order. The main purpose of this paper consists in refining the analysis and providing a sharper estimate for both time and space errors. More precisely, we improve the error estimates by giving a more accurate coefficient in the time error term and removing the factor in the space error term, which grows with decreasing time step. Then the theoretical results are validated by a number of numerical tests.
引用
收藏
页码:384 / 400
页数:17
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