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The two-dimensional unsteady coupled Burgers' equations with moderate tosevere gradients, are solved numerically using higher-order accurate finitedifference schemes; namely the fourth-order accurate compact ADI scheme, andthe fourth-order accurate Du Fort Frankel scheme. The question of numericalstability and convergence are presented. Comparisons are made between thepresent schemes in terms of accuracy and computational efficiency for solvingproblems with severe internal and boundary gradients. The present study showsthat the fourth-order compact ADI scheme is stable and efficient

On the Fourth-Order Accurate Compact ADI Scheme for Solving the Unsteady Nonlinear Coupled Burgers' Equations