分数阶对流扩散方程的半加权有限差分格式

朱琳; 芮洪兴

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分数阶对流扩散方程的半加权有限差分格式

朱琳^,,
芮洪兴

1.
宁夏大学~~数学与计算机学院, 银川750021;
2.
山东大学~~数学学院, 济南250100

基金项目:

国家自然科学基金(11171190, 11161036); 宁夏自然科学基金(NZ14233)

详细信息

作者简介:
朱琳, 女, 副教授, 研究方向为偏微分方程数值解. E-mail: xqdeng2002@163.com

通讯作者:
朱琳, 女, 副教授, 研究方向为偏微分方程数值解.

中图分类号: O241.82
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- 文章访问数: 577
- HTML全文浏览量: 61
- PDF下载量: 931
- 被引次数: 0
出版历程
- 收稿日期: 2014-11-06
- 刊出日期: 2015-11-25

Semi-weighted finite difference schemes for one dimensiona fractional advection-dispersion equations

ZHU Lin^,,
RUI Hong-Xing

摘要

摘要: 对于空间分数阶对流扩散方程的初边值问题提出了一系列半加权差分格式.可以证明此格式当分数阶导数属于$[(\sqrt{17}-1)/2,2]$时无条件稳定,且二阶收敛. 最后给出数值算例验证了理论证明.
- 半加权有限差分格式 /
- 分数阶对流扩散方程 /
- 无条件稳定
Abstract: A series of semi-weighted implicit finite difference schemes for solving one-dimensional fractional advection-dispersion equations with variable coefficients on a finite domain are considered in this paper. The schemes are proved unconditionally stable and second-order accuracy in spatial grid size for the problem with order of fractional derivative belonging to $[(\sqrt{17}-1)/2,2].$ Numerical examples are provided to verify the theoretical analysis.
- semi-weighted implicit finite difference schemesfractional advection-dispersion equationsunconditionally stable /

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参考文献(1)

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