A Two-Level Fourth-Order Approach For Time-Fractional Convection-Diffusion-Reaction Equation With Variable Coefficients

TL;DR

This paper presents a novel two-level fourth-order numerical scheme for efficiently solving time-fractional convection-diffusion-reaction equations with variable coefficients, demonstrating high accuracy and unconditional stability.

Contribution

The paper introduces a new two-level fourth-order method with proven stability and convergence for time-fractional PDEs with variable coefficients, improving computational efficiency.

Findings

Unconditionally stable numerical scheme with order $O(k^{2-rac{ ext{lambda}}{2}}+h^{4})$

Numerical experiments confirm stability and convergence rates

Method outperforms many existing techniques in efficiency

Abstract

This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new approach are investigated and both stability and error estimates of the proposed numerical scheme are deeply analyzed in the $L^{\infty}(0,T;L^{2})$-norm. The theory indicates that the method is unconditionally stable with convergence of order $O(k^{2-\frac{\lambda}{2}}+h^{4})$, where $k$ and $h$ are time step and mesh size, respectively, and $\lambda\in(0,1)$. This result suggests that the two-level fourth-order technique is more efficient than a large class of numerical techniques widely studied in the literature for the considered problem. Some numerical evidences are provided to verify the unconditional stability and convergence rate of the proposed algorithm.