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Erschienen in:
ODE Models for Systems Biological Networks Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

2. Numerical Simulation of ODE Models

verfasst von : Peter Deuflhard, Susanna Röblitz

Erschienen in: A Guide to Numerical Modelling in Systems Biology

Verlag: Springer International Publishing

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Abstract

In the preceding chapter we had worked out how to establish possibly large ODE models for systems biological networks. In the present chapter, we deal with their numerical simulation. For this purpose, we describe various numerical integrators for initial value problems in necessary detail. In Sect. 2.1, we present basic concepts to characterize different discretization methods. We start with local versus global discretization errors, first in theory, then in algorithmic realization. Stability concepts for discretizations lead to an elementary pragmatic understanding of the term “stiffness” of ODE systems. In the remaining part of the chapter, different families of integrators such as Runge-Kutta methods, extrapolation methods, and multistep methods are characterized. From a practical point of view they are divided into explicit methods (Sect. 2.2), implicit methods (Sect. 2.3), and linearly implicit methods (Sect. 2.4), to be discussed in terms of their structural strengths and weaknesses. Finally, in Sect. 2.5, a roadmap of numerical methods is given together with two moderate problems that look rather similar, but require different numerical integrators. Moreover, we present a more elaborate example concerning the dynamics of tumor cells; therein we show, what kind of algorithmic decisions may influence the speed of computations.

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Vorheriges Kapitel ODE Models for Systems Biological Networks
Nächstes Kapitel Parameter Identification in ODE Models
Fußnoten
1
Moulton published his method not earlier than 1926, since it was regarded as a “military secret” during World War I.
 
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Metadaten
Titel
Numerical Simulation of ODE Models
verfasst von
Peter Deuflhard
Susanna Röblitz
Copyright-Jahr
2015
Buch
A Guide to Numerical Modelling in Systems Biology

Print ISBN: 978-3-319-20058-3

Electronic ISBN: 978-3-319-20059-0

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-20059-0_2