Ordinary Differential Equation Models: Numerical Integration of Initial-Value Problems

François E. Cellier
Institute of Computational Science
ETH Zürich
CH-8092 Zürich
Switzerland
Email: FCellier@Inf.ETHZ.CH

Abstract

Although the concept of ordinary differential equations (ODEs) as modeling formalism is quite old (see Simulation Modeling Formalism: Ordinary Differential Equations), only the advent of modern computer technology has made ODEs solvable in a very general sense. In this article, we shall try to classify some of the more popular numerical integration schemes. As there does not exist any numerical integration algorithm which is equally well suited to all types of ODE models, we shall also try to classify the models to some extent.

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