Application of functional optimization techniques for the serial hybrid computer solution of partial differential equations

Since its introduction in 1961, the serial or CSDT (continuous-space-discrete-time) method for solving nonlinear parabolic partial differential equations in one space-dimension has received a considerable amount of attention. This effort has been justified by the engineering importance and the abundance of problems characterized by one-dimensional diffusion equations. Although initially introduced as a pure analog technique, interest in the CSDT method was stimulated particularly by the increasing availability and capabilities of hybrid computing systems. Utilizing the hybrid computer, a closed loop of analog elements is employed to integrate a second-order ordinarly differential equation at successive time levels. The digital computer serves as a function memory and to control the iterative determination of an initial condition at each time level.