Numerical Methods for Ordinary Differential Equations
Chapter One
Differential and Difference
Equations
10 Differential Equation Problems
100 Introduction to differential equations
As essential tools in scientific modelling, differential equations are familiar to
every educated person. In this introductory discussion we do not attempt to
restate what is already known, but rather to express commonly understood
ideas in the style that will be used for the rest of this book.
The aim will always be to understand, as much as possible, what we expect
to happen to a quantity which satisfies a differential equation. At the most
obvious level, this means predicting the value this quantity will have at some
future time. However, we are also interested in more general questions such
as the adherence to possible conservation laws or perhaps stability of the
long-term solution. Since we emphasize numerical methods, we often discuss
problems with known solutions mainly to illustrate qualitative and numerical
behaviour.
Even though we sometimes refer to 'time' as the independent v ... read full excerpt from Numerical Methods for Ordinary Differential Equations ebook
