On the Stability of Numerical Integration Routines for Ordinary Differential Equations

Numerical integration methods for the solution of initial valueproblems for ordinary vector differential equations may be modelledas discrete time feedback systems. The stability criteria discoveredin modern control theory are applied to these systems and criteriainvolving the routine, the step size and the differential equationare derived. Linear multistep, Runge-Kutta, and predictor-correctormethods are all investigated.