Two difference schemes for solving the one-dimensional time distributed-order fractional wave equations

被引：22

作者：

Gao, Guang-hua ^{[1
]}

Sun, Zhi-zhong ^{[2
]}

机构：

[1] Nanjing Univ Posts & Telecommun, Coll Sci, Nanjing 210023, Jiangsu, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2017年 / 74卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Distributed order; Fractional derivative; Difference scheme; Stability; Convergence; DIFFUSION-EQUATIONS; NUMERICAL APPROXIMATION; EXTRAPOLATION METHOD;

D O I：

10.1007/s11075-016-0167-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Two difference schemes are derived for numerically solving the one-dimensional time distributed-order fractional wave equations. It is proved that the schemes are unconditionally stable and convergent in the norm with the convergence orders O(tau (2) + h (2)+Delta gamma (2)) and O(tau (2) + h (4)+Delta gamma (4)), respectively, where tau,h, and Delta gamma are the step sizes in time, space, and distributed order. A numerical example is implemented to confirm the theoretical results.

引用

页码：675 / 697

页数：23

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