Abstract
For the numerical solution of initial value problems for systems of ODEs there are many methods available, such as Runge-Kutta methods and linear multistep methods. In this chapter we give examples of methods which are of interest in the discretization of time-dependent PDEs. We will confine ourselves to methods having a low to moderate order. Further we pay attention to properties of specific interest to PDEs, namely the positivity property and the accuracy behaviour of Runge-Kutta methods for initial-boundary value problems. Excellent general references on ODE methods are Lambert (1991), Hairer, N0rsett & Wanner (1993) and Hairer & Wanner (1996).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hundsdorfer, W., Verwer, J. (2003). Time Integration Methods. In: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations. Springer Series in Computational Mathematics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-09017-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-09017-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05707-6
Online ISBN: 978-3-662-09017-6
eBook Packages: Springer Book Archive