中文摘要：

In this paper,we study an efficient higher order numerical method to timefractional 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.

英文摘要：

In this paper, we study an efficient higher order numerical method to timefractional 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.