Simulations of the poisson type partial differential equations where the nodes are bound by the knight's moves

It is very much desired to have subsystems resulting from finite difference modeling of partial differential equations where the matrices are block diagonal as the work required to solve such subsystems is reduced greatly. The simulation nodes in the red/black order and bound by the usual five-point finite difference molecule have their coefficient matrix with such pattern. In this paper, we attempt to have such subsystems for the coefficient matrix for the nodes bound by the nine-point molecule. This can be accomplished by the knight's move. A comparison of the performances between this model and the usual nine-point model is given. We note that the coefficient matrix favors the acceleration of the basic iterative methods.