Sinc Collocation Method For Time Fractional Second Order Partial Differential Equation

With the rapid development and wide application of fractional differential equations in many scientific fields,a large number of scholars have paid attention to the numerical solution of the time-fractional partial differential equations.At present,the numerical methods for solving time-fractional partial differential equations mainly focus on finite difference method,finite element method,spectral method,orthogonal spline collocation method,etc.This paper mainly considers the Sinc Collocation method to solve the problem of time fractional partial differential equations.First,the finite difference method is used to give the time semi-discrete format of the equation in the time direction,and the stability and convergence of the semi-discrete format are proved.Then we use the Sinc Collocation method to deal with the spatial direction derivatives,and get the full discrete format of the equation.Finally,in the numerical example,the feasibility and efficiency of the Sinc Collocation method are verified by comparing the exact solution with the numerical solution.