Abstract
A derivation is presented, based on APL thinking, of a numerical method for solving discrete Poisson equations in a rectangle. The method is equivalent to Separation of Variables, as it must be. It was recovered by this author during the recoding, in APL, of the world's first numerical weather forecast code, von Neumann had presented a formula in 1950, without derivation, for the solution of this type of Elliptic Partial Differential Equation. After using APL to derive the formula, this author then shows the formula equivalent to a Tensor Product method suggested by Lynch, Rice, and Thomas, [2], 14 years after von Neumann's paper. The APL derivation is new and helpful in understanding the structure of the Separation of Variables solution. The derivation depends on APL thinking and manipulations that are not standard in Applied Mathematics.