非线性变阶分数阶扩散方程的全隐差分格式

J4 ›› 2013, Vol. 48 ›› Issue (2): 93-97.

非线性变阶分数阶扩散方程的全隐差分格式

马维元,张海东,邵亚斌

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:2012-09-04 出版日期:2013-02-20 发布日期:2013-03-04
作者简介:马维元(1980- ),男,讲师,硕士,研究方向为微分方程数值解法. Email:mwy2004@126.com
基金资助:
国家自然科学基金资助项目 (11161041);中央高校基本科研业务专项资金(zyz2012076);西北民族大学中青年科研基金项目(12XB29)

Fully implicit finite difference scheme for the variable-order nonlinear fractional diffusion equation

MA Wei-yuan, ZHANG Hai-dong, SHAO Ya-bin

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

Received:2012-09-04 Online:2013-02-20 Published:2013-03-04

摘要/Abstract

摘要：

对于变阶的非线性分数阶扩散方程,提出了一种全隐的差分格式。然后,通过离散的能量方法证明了所提出的格式是无条件稳定的,其收敛阶为O(τ+h)。通过数值试验表明,全隐的差分格式是有效的和可靠的。

关键词: 变阶的非线性分数阶扩散方程;全隐的差分格式;迭代算法;收敛性;稳定性

Abstract:

A fully implicit finite difference scheme for the variable-order nonlinear fractional diffusion equation is considered. It is shown that the method is unconditional stable by discrete energy method. The convergence order of the method is O(τ+h). Numerical results demonstrate that the method is efficient and reliable.

Key words: variable-order nonlinear fractional diffusion equation; fully implicit difference scheme; iterative algorithm; convergence; stability

马维元,张海东,邵亚斌. 非线性变阶分数阶扩散方程的全隐差分格式[J]. J4, 2013, 48(2): 93-97.

MA Wei-yuan, ZHANG Hai-dong, SHAO Ya-bin. Fully implicit finite difference scheme for the variable-order nonlinear fractional diffusion equation[J]. J4, 2013, 48(2): 93-97.

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