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

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.

37 pages, 4 tables, 16 figures

References in corpus (4)

• A Time-Split MacCormack Scheme for Two-Dimensional Nonlinear Reaction-Diffusion Equations
• An efficient explicit approach for predicting the Covid-19 spreading with undetected infectious: The case of Cameroon
• A Novel Three-Level Time-Split MacCormack Method for Solving Two-Dimensional Viscous Coupled Burgers Equations
• Error Estimate of MacCormack Rapid Solver Method for 2D Incompressible Navier-Stokes Problems