An Eighth-Order Numerical Method for Spatial Variable-Coefficient Time-Fractional Convection–Diffusion–Reaction Equations - Yuelong Feng; Xindong Zhang; Leilei Wei (Fractal and Fractional)
In this paper, we propose a high-order compact difference scheme for a class of time-fractional convection–diffusion–reaction equations (CDREs) with variable coefficients. Using the Lagrange polynomial interpolation formula for the time-fractional derivative and a compact finite difference approximation for the spatial derivative, we establish an unconditionally stable compact difference method. The stability and convergence properties of the method are rigorously analyzed using the Fourier method. The convergence order of our discrete scheme is <semantics>O(τ4−α+h8)</semantics>, where <semantics>τ</semantics> and h represent the time step size and space step size, respectively. This work contributes to providing a better understanding of the dependability of the method by thoroughly examining convergence and conducting an error analysis. Numerical examples demonstrate the applicability, accuracy, and efficiency of the suggested technique, supplemented by comparisons with previous research.