Algorithms and software for ordinary differential equations and differential-algebraic equations, part I: Euler methods and error estimation

Abstract

Through constructing a mathematical model and computing solutions to it, acquiring insight into a physical process is usually accomplished. Such a model, frequently takes the form of a system of differential equations that govern the behavior of the relevant physical variables as a function of time. In this regard, some of the more important issues in solving problems are identified involving differential equations, shown are how these ideas lead to various kinds of solution methods, and outlined are the current state of research work in these areas.