时间分数阶色散方程的高阶差分方法High Order Finite Difference Method for the Time Fractional Dispersive Equation
谢树森,王辉
摘要(Abstract)：
时间分数阶色散方程用以描述带有记忆性的色散现象。本文研究分数阶色散方程的高精度差分方法,利用紧致差分格式的构造技巧,得到了求解时间分数阶色散方程的四点四阶和五点六阶2个紧致隐式差分格式,收敛阶分别为O(τ2+h4)和O(τ2+h6).数值算例表明本文方法是高精度有效的,且具有很好的数值稳定性。
关键词(KeyWords)： 分数阶色散方程;紧致差分格式;高精度
基金项目(Foundation):
作者(Author): 谢树森,王辉
DOI: 10.16441/j.cnki.hdxb.2013.10.019
参考文献(References)：
- [1]Podlubny Igor.Fractional Differential Equations[M].New York:Academic Press,1999.
- [2]Chen Changming,Liu F,Burrage K.Finite difference methods and a fourier analysis for the fractional reaction-subdiffusion equation[J].Applied Mathematics and Computation,2008,198:754-769.
- [3]金承日,潘有思.时间分数阶色散方程的有限差分方法[J].黑龙江大学学报:自然科学版,2011,28(3):291-294.
- [4]王文洽.色散方程的一类新的并行交替分段隐格式[J].计算数学,2005,27(2):129-140.
- [5]Zhu Shaohong,Zhao Jennifer.The alternating segment explicitimplicit scheme for the dispersive equation[J].Applied Mathematics Letters,2001,14(6):657-662.
- [6]Zhang Qingjie,Wang Wenqia.A four-order alternating segment Crank-Nicolson scheme for the dispersive equation[J].Computers and Mathematics with Applications,2009,57(2):283-289.
- [7]Jiang Yingjun,Ma Jingtang.High-order finite element methods for time-fractional partial differential equations[J].Journal of computational and Applied Mathematics,2011,235(11):3285-3290.
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