An Efficient Algorithm with High Accuracy for Time-Space Fractional Heat Equations

Abstract

In this article, a second-order-accuracy algorithm is proposed for solving time-space fractional heat equations (TSFHEs) in one and two dimensions. The new algorithm combines the product integration method for the fractional integral part with the second-order-accuracy approximation for the space fractional derivatives based on the special transformation of the original problem. Moreover, an alternating direction implicit scheme is presented for the two-dimensional case. Numerical experiments are carried out to verify the accuracy and efficiency of the proposed algorithm.