An Alternating Direction Implicit (ADI), Approximate Factorization (AF) scheme is presented here for the solution of the two-dimensional elliptic partial differential equations, with control functions as source terms, used for grid generation. This scheme requires significantly less computational effort than a Successive Over Relaxation (SOR) scheme. The dependence of the choice of the acceleration parameter on the rate of convergence of the AF scheme has been studied. As an example, grids generated by this method are shown, along with a comparison of the convergence history for the present AF and SOR schemes.

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