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Teaching Mathematics and its Applications Advance Access published online on February 10, 2008
Teaching Mathematics and its Applications, doi:10.1093/teamat/hrm021
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© The Author 2008. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Matrix solution of coupled differential equations and looped car following models

Mark McCartney

Address for Correspondence: School of Computing and Mathematics, University of Ulster, Newtownabbey, Co. Antrim, Northern Ireland, BT37 0QB, UK.

Submitted May 2007; accepted December 2007

A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help students engage with the model and its solution. The material is suitable for use as part of a first course in differential equations at undergraduate level.

Dr Mark McCartney is a lecturer in Mathematics at the University of Ulster. His interests include the modeling of traffic dynamics and the history of science.


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