A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative

This paper considers a high-order numerical method for a computed solution of multidimensional convection-diffusion-reaction equation with time-fractional deriva -tive subjected to appropriate initial and boundary conditions. The stability and error estimates of the proposed numerical approach are analyzed using the L-infinity(0, T ; L-2)-norm. The theoretical study suggests that the new technique is unconditionally stable and temporal accurate with order O(tau(2+alpha)), where tau denotes the time step and 0 < alpha < 1. This result shows that the developed algorithm is faster and more effi-cient than a broad range of numerical techniques widely studied in the literature for the considered problem. Numerical experiments confirm the theory and they indicate that the proposed numerical scheme converges with accuracy O (tau(2+alpha) + h(4)), where h represents the space step.

Automated summary

This paper proposes a high-order numerical method for solving the multidimensional convection-diffusion-reaction equation with time-fractional derivative. The stability and error estimates of the method are analyzed, showing its unconditional stability and temporal accuracy of order O(tau(2+alpha)), where tau is the time step and 0 < alpha < 1. Numerical experiments confirm the theory and demonstrate the convergence accuracy of the proposed scheme to be O(tau(2+alpha) + h(4)), with h representing the space step.