Efficient Evaluation of the Liouville-Caputo Fractional Derivative for TFCRD Equations

Abstract

For the variable coefficient Time-Fractional Convection-Reaction-Diffusion (TFCRD) equation, a fast compact finite difference scheme based on an efficient and high-order accurate numerical formulation to accelerate the computation of Liouville-Caputo derivatives is presented. The proposed method led to speed up the evaluation of the Liouville-Caputo fractional derivative based on the L2−1_δ when compared to the numerical solution of the variable coefficient TFCRD equation given by directly evaluating L2−1_δ formula. The proposed difference scheme not only maintains unconditional stability and high accuracy, but also significantly reduces storage requirements and computational costs. Numerical experiments confirm the theoretical analysis.