A finite difference method based scheme incorporating a method of false transients and an approximate factorisation technique is presented for solution of a system of Poisson's equations used for grid generation. A time step cycling process with repeated endpoints enhances the convergence rate. The scheme required much less computational effort than that required by other numerical schemes. High quality grid systems over an aircraft tailplane are presented. Although, the superiority of the scheme is illustrated for the grid generation problem, it can be employed for other problems requiring the solution of a set of similar elliptic partial differential equations.