两边空间-时间分数阶扩散方程的加权有限差分格式

华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 41-48,70.

两边空间-时间分数阶扩散方程的加权有限差分格式

马维元, 刘华

西北民族大学~~数学与计算机科学学院, 甘肃兰州 730030

收稿日期:2011-03-01 修回日期:2011-06-01 出版日期:2012-05-25 发布日期:2012-05-22

Weighted finite difference methods for two-sided space-time fractional diffusion equations

MA Wei-yuan, LIU Hua

School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, China

Received:2011-03-01 Revised:2011-06-01 Online:2012-05-25 Published:2012-05-22

摘要/Abstract

摘要： 对于空间-时间分数阶扩散方程的初边值问题提出了一种加权差分格式. 利用能量估计, 得到了差分格式的稳定性. 然后使用数学归纳法证明了在相同的条件下, 所提出的的格式是收敛的. 最后通过一个例子说明了所提出的格式是可靠的、有效的.

关键词: 分数阶扩散方程, 空间-时间分数阶导数, 加权差分格式, 收敛性, 稳定性

Abstract: A weighted finite difference scheme was proposed in order to solve initial-boundary value problems of space-time fractional diffusion equations. Their stability was analyzed by means of discrete energy method. Using mathematical induction, we proved that the scheme was convergent under the same condition. Illustrative
example was included to demonstrate the validity and applicability of the scheme.

Key words: fractional diffusion equation, space-time fractional derivative, weighted difference scheme, convergence, stability

中图分类号:

O241.82

马维元, 刘华. 两边空间-时间分数阶扩散方程的加权有限差分格式[J]. 华东师范大学学报(自然科学版), 2012, 2012(3): 41-48,70.

MA Wei-yuan, LIU Hua. Weighted finite difference methods for two-sided space-time fractional diffusion equations[J]. Journal of East China Normal University(Natural Sc, 2012, 2012(3): 41-48,70.

参考文献

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