Numerical Initial Value Problems in Ordinary Differential Equations

The theoretical physicist or chemist spends much of his time working with models of the world around him. A model is often given as a mathematical description of variables, some of which certainly exist and are measurable (pressure, for example), others of which may only be hypothesized (the characteristics of a new particle, for example). Frequently these models will be sets of ordinary differential equations in which the independent variable is time and the dependent variables are the physical variables. Occasionally the independent variable may be one of the physical variables due either to an interchange of variables, or the solution of a system in equilibrium state which is therefore independent of time, but we will call the independent variable t time throughout this book. The methods to be discussed are not dependent on any special property of time, so that the reader should be prepared to substitute x for space or whatever meets his fancy.