An Analog Computer Technique for Solving a Class of Nonlinear Ordinary Differential Equations

A technique for solving a set of ordinary nonlinear differential equations of the form d Yi/d X = fi(Yi)gi(Y1, Y2, ..., Yn, X) is discussed. Sets of equations of this form describe such phenomena as heat transfer with variable specific heat, solid propellant burning with variable burning area, and chemical decomposition reactions with variable reagent temperatures. The technique is applicable to digital or analog computation; however, this paper deals only with its application to analog computing. An analog computer mechanization of one equation of the set, using the technique discussed, is illustrated and compared to the standard straightforward mechanization of the same equation. Comparison of the two mechanizations shows that one multiplier may be eliminated from the mechanization of each equation of the set by utilizing the alternate technique presented in this paper. If the set is large, this can result in significant equipment savings. Results from an example three-node heat transfer problem solved with the standard mechanization are compared with results obtained when the same system is solved by the alternate scheme proposed in this paper. The comparison shows that the two solutions are in good agreement.