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时间分数阶扩散方程的一个新的高阶数值格式

王自强, 曹俊英   

  1. 贵州民族大学理学院, 贵阳, 550025
  • 收稿日期:2014-03-20 出版日期:2014-12-15 发布日期:2014-12-08
  • 基金资助:

    国家自然科学基金(2010CB832702,11426074);贵州省科技厅自然科学基金([2014]2098,[2013]2144);贵州省教育厅([2013]405).

王自强, 曹俊英. 时间分数阶扩散方程的一个新的高阶数值格式[J]. 数值计算与计算机应用, 2014, 35(4): 277-288.

Wang Ziqiang, Cao Junying. A NEW HIGH ORDER NUMERICAL SCHEME TO THE TIME FRACTIONAL DIFFUSION EQUATIONS[J]. Journal of Numerical Methods and Computer Applications, 2014, 35(4): 277-288.

A NEW HIGH ORDER NUMERICAL SCHEME TO THE TIME FRACTIONAL DIFFUSION EQUATIONS

Wang Ziqiang, Cao Junying   

  1. College of Science, Guizhou Minzu University, 550025 Guiyang, China
  • Received:2014-03-20 Online:2014-12-15 Published:2014-12-08
研究时间分数阶扩散方程, 利用时间方向的有限差分格式和空间方向的Legendre collocation谱方法构造了一个高阶稳定格式.一系列的数值试验表明该格式是稳定的, 其收敛阶为Ot3-α+N-m), 这里α, Δt, Nm分别为时间分数阶导数的阶数、时间步长、空间多项式逼近阶数和精确解的正则度.
We investigate the time fractional anomalous diffusion equation on a bounded domain. We propose an efficient method for its numerical solution. This method is based on a finite difference in time and spectral method in space. The numerical examples show the convergence rate is Ot3-α+N-m), where αt,N and m are respectively the order of time fractional derivatives, time step size, the polynomial degree and the regularity of the exact solution.

MR(2010)主题分类: 

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