In this book we discuss several numerical methods for solving ordinary differential equations. We emphasize the aspects that play an important role in practical problems. We conﬁne ourselves to ordinary differential equations with the exception of the last chapter in which we discuss the heat equation, a parabolic partial differential equation. The techniques discussed in the intro-ductory chapters, for instance interpolation, numerical quadrature and the solution to nonlinear equations, may also be used outside the context of differential equations. They have been in-cluded to make the book self-contained as far as the numerical aspects are concerned. Chapters, sections and exercises marked with a * are not part of the Delft Institutional Package.
The numerical examples in this book were implemented in Matlab, but also Python or any other programming language could be used. A list of references to background knowledge and related literature can be found at the end of this book.
This open book is licensed under a Creative Commons License (CC BY). You can download Numerical Methods for Ordinary Differential Equations ebook for free in PDF format (2.0 MB).
Table of Contents
Numberical time integration of initial-value problems
The finite-difference method for boundary-value problems
The instationary heat equation
Numerical Methods for Ordinary Differential Equations
Science and Mathematics
TU Delft Open
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