留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

变系数分数阶对流扩散方程的一种算子矩阵方法

朱晓钢 聂玉峰

朱晓钢, 聂玉峰. 变系数分数阶对流扩散方程的一种算子矩阵方法[J]. 应用数学和力学, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041
引用本文: 朱晓钢, 聂玉峰. 变系数分数阶对流扩散方程的一种算子矩阵方法[J]. 应用数学和力学, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041
ZHU Xiaogang, NIE Yufeng. An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients[J]. Applied Mathematics and Mechanics, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041
Citation: ZHU Xiaogang, NIE Yufeng. An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients[J]. Applied Mathematics and Mechanics, 2018, 39(1): 104-112. doi: 10.21656/1000-0887.380041

变系数分数阶对流扩散方程的一种算子矩阵方法

doi: 10.21656/1000-0887.380041
基金项目: 国家自然科学基金(11471262; 11501450)
详细信息
    作者简介:

    朱晓钢(1987—),男,博士生(E-mail: zhuxg590@yeah.net);聂玉峰(1968—),男,教授,博士生导师(通讯作者. E-mail: yfnie@nwpu.edu.cn).

  • 中图分类号: O241.8

An Operational Matrix Method for Fractional Advection-Diffusion Equations With Variable Coefficients

Funds: The National Natural Science Foundation of China(11471262; 11501450)
  • 摘要: 研究带Caputo分数阶导数的变系数对流扩散方程的数值解法.基于Chebyshev cardinal函数,推导RiemannLiouville分数阶积分的一个有效算子矩阵,以之为基础,提出了变系数分数阶对流扩散方程的一种新的算子矩阵法.该方法将方程的求解转化成矩阵的代数运算,具有计算量小和易于编程等特点.给出数值算例并与一些现有的方法进行比较,结果表明该方法是收敛的且在计算精度上占有优势.
  • [1] ICHISE M, NAGAYANAGI Y, KOJIMA T. An analog simulation of non-integer order transfer functions for analysis of electrode processes[J]. Journal of Electroanalytical Chemistry and Interfacial Electrochemistry,1971,33(2): 253-265.
    [2] COLE K S. Electric conductance of biological systems[J]. Cold Spring Harbor Symposia on Quantitative Biology,1933,1: 107-116.
    [3] ZHUANG P, LIU F. Implicit difference approximation for the time fractional diffusion equation[J]. Journal of Applied Mathematic and Computing,2006,22(3): 87-99.
    [4] 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.
    [5] LIN Yumin, XU Chuanjun. Finite difference/spectral approximations for the time-fractional diffusion equation[J]. Journal of Computational Physics,2007,225(2): 1533-1552.
    [6] MUSTAPHA K, ABDALLAH B, FURATI K M, et al. A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients[J]. Numerical Algorithms,2016,73(2): 517-534.
    [7] YASEEN M, ABBAS M, ISMAIL A I, et al. A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations[J]. Applied Mathematics and Computation,2017,293: 311-319.
    [8] CUI Ming-rong. Compact finite difference method for the fractional diffusion equation[J]. Journal of Computational Physics,2009,228(20): 7792-7804.
    [9] LIU Q, GU Y T, ZHUANG P, et al. An implicit RBF meshless approach for time fractional diffusion equations[J]. Computational Mechanics,2011,48(1): 1-12.
    [10] IZADKHAH M M, SABERI-NADJAFI J. Gegenbauer spectral method for time-fractional convection-diffusion equations with variable coefficients[J]. Mathematical Methods in the Applied Sciences,2015,38(15): 3183-3194.
    [11] SAADATMANDI A, DEHGHAN M, AZIZI M-R. The Sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients[J]. Communications in Nonlinear Science and Numerical Simulation,2012,17(11): 4125-4136.
    [12] GHANDEHARI M A M, RANJBAR M. A numerical method for solving a fractional partial differential equation through converting it into an NLP problem[J]. Computers & Mathematics With Applications,2013,65(7): 975-982.
    [13] CHEN Y M, WU Y B, CUI Y H, et al. Wavelet method for a class of fractional convection-diffusion equation with variable coefficients[J]. Journal of Computational Science,2010,1(3): 146-149.
    [14] BHRAWY A H, ZAKY M. A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients[J]. Mathematical Methods in the Applied Sciences,2016,39(7): 1765-1779.
    [15] NEMATI S, SEDAGHAT S. Matrix method based on the second kind Chebyshev polynomials for solving time fractional diffusion-wave equations[J]. Journal of Applied Mathematics and Computing,2016,51(1/2): 189-207.
    [16] DOHA E H, BHRAWY A H, EZZ-ELDIEN S S. An efficient Legendre spectral Tau matrix formulation for solving fractional subdiffusion and reaction subdiffusion equations[J]. Journal of Computational and Nonlinear Dynamics,2015,10(2): 021019. DOI: 10.1115/1.4027944.
    [17] Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations [M]. Amsterdam: Elsevier Science, 2006.
    [18] Boyd J P. Chebyshev and Fourier Spectral Methods [M]. Mineola: Dover Publications Inc, 2001.
    [19] PANG Guofei, CHEN Wen, FU Zhoujia. Space-fractional advection—dispersion equations by the Kansa method[J].Journal of Computational Physics,2015,293: 280-296.
    [20] ELHAY S, KAUTSKY J. Algorithm 655: IQPACK: FORTRAN subroutines for the weights of interpolatory quadratures[J]. ACM Transactions on Mathematical Software,1987,13(4): 399-415.
    [21] GAUTSCHI W. High-order Gauss-Lobatto formulae[J]. Numerical Algorithms,2000,25(1): 213-222.
  • 加载中
计量
  • 文章访问数:  1175
  • HTML全文浏览量:  202
  • PDF下载量:  763
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-02-23
  • 修回日期:  2047-03-19
  • 刊出日期:  2018-01-15

目录

    /

    返回文章
    返回