Numerical Integration of Systems of Stiff Nonlinear Differential Equations

Abstract

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 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ). The approach is developed in a way which provides some detailed understanding of why it is useful.