Collocation Method for Time Fractional Diffusion Equation Based on the Chebyshev Polynomials of Second Kind

Abstract

This paper deals with the numerical solution for a class of time-fractional diffusion equations (TFDE). The fractional time derivative is considered in the Caputo sense of order $$\mu (0<\mu \le 1)$$ . Finite difference approximation is used for time derivative, while Chebyshev polynomials of the second kind are used to approximate the space derivative. The given scheme is simple in use for solving TFDE since the given boundary and initial conditions are taken into account automatically. The advantages of the proposed scheme are its exponential convergence and low computational cost. Also, we discuss error analysis and convergence of the suggested scheme for solving TFDE. The given scheme is examined through some examples and comparison are provided with existed methods which show the efficiency and accuracy of proposed scheme.