NUMERICAL INTEGRATION OF SYSTEMS OF STIFF NONLINEAR DIFFERENTIAL EQUATIONS

In connection with the design of transistor circuits, for example, it is frequently necessary to obtain a numerical solution of a system of nonlinear ordinary differential equations. In some cases, these equations possess a property that leads to intolerable computational requirements relative to the use of standard predictor‐corrector techniques or general linear multipoint formulas of open type. Here we describe an alternative approach which has been used to solve some practical problems by permitting dramatic step‐size increases (for example, a factor of 104). The approach is developed in a way which provides some detailed understanding of why it is useful. © 1968 The Bell System Technical Journal