  In this paper, we analyze the three-level explicit time-split MacCormack
procedure in the numerical solutions of two-dimensional viscous coupled
Burgers' equations subject to initial and boundary conditions. The differential
operators split the two-dimensional problem into two pieces so that the
two-step explicit MacCormack scheme can be easily applied to each subproblem.
This reduces the computational cost of the algorithm. For low Reynolds numbers,
the proposed method is second order accurate in time and fourth convergent in
space, while it is second order convergent in both time and space for high
Reynolds numbers problems. This shows the efficiency and effectiveness of the
considered method compared to a large set of numerical schemes widely studied
in the literature for solving the two-dimensional time dependent nonlinear
coupled Burgers' equations. Numerical examples which confirm the theoretical
results are presented and discussed.
