Mixed Generalized Jacobi and Chebyshev Collocation Method for Time-Fractional Convection-Diffusion Equations
Received:November 19, 2015  Revised:July 29, 2016
Key Words: time-fractional convection-diffusion equations   collocation methods   shifted generalized Jacobi functions   shifted Chebyshev polynomials  
Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11401380; 11671166).
Author NameAffiliation
Tao SUN School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, P. R. China 
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      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.
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