The Automatic Integration of Ordinary Differential Equations An integration technique for the automatic solution of an initial value problem for a set of ordinary differential equations is described. A criterion for the selection of the order of approximation is proposed. The objective of the criterion is to increase the step size so as to reduce solution time. An option permits the solution of "stiff" differential equations. A program embodying the techniques discussed appears in Algorithm 407. CACM March, 1971 Gear, C. W. differential equations, stiff equations, integration, step control, order control 5.17 CA710305 JB February 3, 1978 4:28 PM 2205 5 2207 2207 5 2207 2207 5 2207 2207 5 2207 2474 5 2207 2205 6 2207 2207 6 2207 2207 6 2207