A novel three-level time-split MacCormack scheme for two-dimensional evolutionary linear convection-diffusion-reaction equation with source term
Eric Ngondiep
Abstract
This study presents a three-level explicit time-split MacCormack method to compute approximate solutions of two-dimensional time-dependent linear convection-diffusion-reaction equations with source term. The difference operators split the two-dimensional problem into two pieces so that each subproblem is easily solvable using the original MacCormack approach. Second order accuracy in time and fourth-order convergence in space are achieved by the application of the Taylor series expansion. The proposed algorithm minimizes the computational time, computer memory requirement and is easy to implement. Under a suitable time-step restriction, both stability and error estimates of the numerical scheme are deeply analysed in L∞(0,T;L2)-norm. Numerical evidences which confirm the theoretical analysis are considered and discussed.