A two-level fourth-order approach for time-fractional convection–diffusion–reaction equation with variable coefficients

This paper develops a two-level fourth-order scheme for solving time-fractional convection–diffusion–reaction equation with variable coefficients subjects 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∞(0,T;L2)-norm. The theory indicates that the method is unconditionally stable with convergence of order O(k2−λ2+h4), where k and h are time step and mesh size, respectively, and λ∈(0,1). This result suggests that the two-level fourth-order procedure 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. •Detailed description of a two-level fourth-order approach for time-fractional problem.•Proof of basis properties of the proposed approach.•Proof of unconditional stability and convergence rate of the new algorithm.•Some numerical experiments.