Numerical Methods for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations

Vuik, Cornelis (TU Delft Delft Institute of Applied Mathematics)
Vermolen, F.J. (University of Hasselt)
van Gijzen, M.B. (TU Delft Numerical Analysis)
Vuik, Thea (VORtech)

Delft Institute of Applied Mathematics

2023

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. Extra information about this course can be found at http://NMODE.ewi.tudelft.nl, among which old exams, answers to the exercises, and a link to an online education platform. We thank Matthias Moller for his thorough reading of the draft of this book and his helpful suggestions.

numerical methods
differential equations
numerical integration
interpolation
nonlinear equations

http://resolver.tudelft.nl/uuid:ffa6e392-2b54-4db2-bd95-12bf037094ab

https://doi.org/10.5074/t.2023.001

TU Delft Open

978-94-6366-665-7

This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY)

Institutional Repository

book

© 2023 Cornelis Vuik, F.J. Vermolen, M.B. van Gijzen, Thea Vuik