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空间四阶的时间亚扩散方程的有限差分方法 被引量：2

Finite difference methods for time subdiffusion equation with space fourth-order
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摘要 提出了两个求解空间四阶的时间亚扩散方程的数值方法,其误差阶分别为O(τ+h^2)和O(τ~2+h^2).通过Fourier方法,发现两个差分格式均为无条件稳定的.最后,通过数值例子,验证了两个算法的有效性. Two numerical schemes for a time subdiffusion equation with space fourth-order are proposed, and the convergence orders are O（τ＋h2） and O（τ2＋h2）, respectively. By using the Fourier method, it is found that two finite difference schemes are all unconditionally stable. Finally, numerical examples are given to testify the efficiency of the numerical schemes.
作者 郭建 李常品 丁恒飞
机构地区 上海大学理学院
出处 《应用数学与计算数学学报》 2014年第1期96-108,共13页 Communication on Applied Mathematics and Computation
基金 国家自然科学基金资助项目(11372130) 上海市教育委员会科研创新重点资助项目(12ZZ084)
关键词 分数阶 Fourier方法 亚扩散方程 有限差分方法 fractional order Fourier method subdiffusion equation finite difference method
分类号 O241.82 [理学—计算数学]
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参考文献20

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共引文献30

同被引文献7

  • 1郭柏灵,蒲学科,黄凤辉.分数阶偏微分方程及其数值解[M].北京:科学出版社,2011.
  • 2陆金甫,关治.偏微分方程数值解法[M].北京:清华大学出版社,2007:82.
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  • 4Podlubny I. Fractional Differential Equations[M]. San Diego: Acdemic Press, 1999.
  • 5Li C P, Chen A, Ye J J. Numerical approaches to fractional calculus and fractional ordinary differential equation[J]. Journal of Computational Physics, 201,230(9): 3352-3368.
  • 6Chen Y H, Yu C Y. A new algorithm for computing the inverse and the determinant of a Hessenberg matrix[J]. Applied Mathe- matics and Computation, 2011, (218): 4433-4436.
  • 7王自强,曹俊英.分数阶扩散方程的一个新的高阶数值格式[J].数学的实践与认识,2015,45(6):315-320. 被引量：1

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应用数学与计算数学学报
2014年 第1期

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