Automatic Digital Programming of Analog Computers

A digital technique for manipulating symbols defining a mathematical expression is introduced and it is shown how this technique can be applied so that a digital computer can automatically compile an analog computer program directly from a mathematical description of the problem to be solved. The mathematical problem considered is that of solving a system of nonlinear first-order differential equations with initial conditions. It is assumed that these equations have been prescaled and are expressed in terms of the physical variables rather than the original mathematical variables. A résumé of a method for reducing the original symbol sequence defining the differential equations to symbol subsequences from which the analog program can be formed is given. It is then shown how the analog program is to be generated from these symbol sequences. To illustrate the detailed application of the technique an analog program is compiled for a particular system of differential equations.