A Hybrid Computer Technique for Treating Nonlinear Partial Differential Equations

When digital computers are employed to solve linear and nonlinear partial differential equations using implicit finite-difference approximations, the most time-consuming portion of the calculation is the solution of the large system of simultaneous difference equations which must be carried out for each time increment. Recognizing that an analog computer system, by virtue of its parallel mode of operation, generates solutions of simultaneous algebraic equations virtually instantaneously regardless of the number of equations involved, a combined analog and digital computer system has been developed. The system includes a small digital computer connected in a closed loop with a network of analog elements, consisting of an array of inexpensive node modules, one for each grid point in space. The purpose of this network is to solve the system of difference equations whenever this solution is required by the digital program. The analog unit, therefore, serves as a subroutine. The resulting system has a number of important advantages over pure digital computer techniques.