孙涛.混合广义Jacobi和Chebyshev谱配置法求解时间分数阶对流扩散方程[J].数学研究及应用,2016,36(5):608~620
混合广义Jacobi和Chebyshev谱配置法求解时间分数阶对流扩散方程
Mixed Generalized Jacobi and Chebyshev Collocation Method for Time-Fractional Convection-Diffusion Equations
投稿时间:2015-11-19  最后修改时间:2016-07-29
DOI:10.3770/j.issn:2095-2651.2016.05.011
中文关键词:  时间分数阶对流扩散方程  谱配置法  移位广义Jacobi函数  移位Chebyshev多项式
英文关键词:time-fractional convection-diffusion equations  collocation methods  shifted generalized Jacobi functions  shifted Chebyshev polynomials
基金项目:国家自然科学基金 (Grant Nos.11401380; 11671166).
作者单位
孙涛 上海立信会计金融学院统计与数学学院, 上海 201209 
摘要点击次数: 551
全文下载次数: 670
中文摘要:
      研究时间Caputo分数阶对流扩散方程的高效高阶数值方法.对于给定的时间分数阶偏微分方程,在时间和空间方向分别采用基于移位广义Jacobi函数为基底和移位Chebyshev多项式运算矩阵的谱配置法进行数值求解.这样得到的数值解可以很好地逼近一类在时间方向非光滑的方程解.最后利用一些数值例子来说明该数值方法的有效性和准确性.
英文摘要:
      In this paper, we study an efficient higher order numerical method to time-fractional partial differential equations with temporal Caputo derivative. A collocation method based on shifted generalized Jacobi functions is taken for approximating the solution of the given time-fractional partial differential equation in time and a shifted Chebyshev collocation method based on operational matrix in space. The derived numerical solution can approximate the non-smooth solution in time of given equations well. Some numerical examples are presented to illustrate the efficiency and accuracy of the proposed method.
查看全文  查看/发表评论  下载PDF阅读器