Jump to ContentJump to Main Navigation
An Introduction to Nonlinear Chemical DynamicsOscillations, Waves, Patterns, and Chaos$
Users without a subscription are not able to see the full content.

Irving R. Epstein and John A. Pojman

Print publication date: 1998

Print ISBN-13: 9780195096705

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195096705.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 03 December 2021

Computational Tools

Computational Tools

Chapter:
(p.138) (p.139) 7 Computational Tools
Source:
An Introduction to Nonlinear Chemical Dynamics
Author(s):

Irving R. Epstein

John A. Pojman

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195096705.003.0012

It is fair to say that the field of nonlinear chemical dynamics would not be where it is today, and perhaps it would not exist at all, without fast digital computers. As we saw in Chapter 1, the numerical simulation of the essential behavior of the BZ reaction (Edelson et al., 1975) did much both to support the FKN mechanism and to make credible the idea that chemical oscillators could be understood without invoking any new principles of chemical kinetics. In 1975, solving those differential equations challenged the most advanced machines of the day, yet the computers used then were less powerful than many of today’s home computers! Despite the present widespread availability of computing power, there remain many challenging computational problems in nonlinear dynamics, and even seemingly simple equations can be difficult to solve or maybe even lead to spurious results. In this chapter, we will look at some of the most widely used computational techniques, try to provide a rudimentary understanding of how the methods work (and how they can fail!), and list some of the tools that are available. There are several reasons for utilizing the techniques described in this chapter: 1. For a complicated system, it is generally not possible to measure all of the rate constants in a proposed mechanism. One way to estimate the remaining parameters is to simulate numerically the behavior of the system, varying the unknown rate constants until the model satisfactorily reproduces the experimental behavior. 2. If a mechanism, which may consist of dozens of elementary chemical reactions, is valid, then it should reproduce the observed dynamical behavior. Proposed mechanisms are most commonly tested by integrating the corresponding rate equations numerically and comparing the results with the experimental time series, or by comparing the results of many such simulations with different initial conditions (or of a numerical continuation study) to the experimental phase diagram. 3. Numerical results can act as a guide to further experiments. The real reason for developing models is not to interpolate between our experimental observations but to extrapolate into unknown realms.

Keywords:   AUTO package, CONT package, Euler's method, GEAR integration package, Matlab, cellular automata, discretization error, explicit integration methods, global error, implicit integration methods

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .