In this paper, we consider the numerical solution of the vorticity transport equation (V.T.E.), which is the basic non- dimensional nonlinear parabolic partial differential equation that governs unsteady flow problem, in two dimensions. We study the alternative direction implicit (A.D.I.) finite difference formula, which can be used to compute the numerical solution for this equation with zero Dirichlet boundary conditions. Moreover, the consistency and the stability of this scheme are discussed. Finally, the approximate solutions and simulations are carried out for a numerical experiment with certain initial functions.
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