Modelling traffic flow: Solving and interpreting differential equations

M McCartney; Malachy Carey

doi:10.1093/teamat/18.3.115

Modelling traffic flow: Solving and interpreting differential equations

M McCartney, Malachy Carey

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.

Original language	English
Pages (from-to)	115-121
Journal	Teaching Mathematics and its Applications
Volume	18
Issue number	3
DOIs	https://doi.org/10.1093/teamat/18.3.115
Publication status	Published - Sep 1999

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McCartney, M., & Carey, M. (1999). Modelling traffic flow: Solving and interpreting differential equations. Teaching Mathematics and its Applications, 18(3), 115-121. https://doi.org/10.1093/teamat/18.3.115

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abstract = "A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.",

author = "M McCartney and Malachy Carey",

note = "Reference text: 1. Wan, F. Y. M., {"}Mathematical Models and Their Analysis.{"} Harper and Row, 1989. 2. Prigogine, I. and Herman, R., {"}Kinetic Theory of Vehicular Traffic.{"} American Elsevier, 1971. 3. Low, D. J. and Addison, P. S., A nonlinear temporal headway model of traffic dynamics, Nonlinear Dynamics, 1998, 16, 127-151. 4. Resnick, M., {"}Turtles, Termites and Traffic Jams.{"} MIT Press, 1995. 5. Paramics web site: http:Hwww.paramics.com/ 6. Tallarida, R. I., {"}Pocket Book of Integrals and Mathematical Formulas.{"} 2/e, CRC Press, 1992. 7. Daganzo, C. F., {"}Fundamentals of Transportation and Traffic Operations.{"} Pergamon, 1999. Downloaded from http://teamat.oxfordjournals.org/ at university of ulster on December 10, 2013",

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doi = "10.1093/teamat/18.3.115",

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AB - A simple mathematical model for how traffic flows along a road is introduced. The resulting first-order ordinary differential equations can be used as an application of solution techniques taught at A-level and first year undergraduate level, and as a motivator to encourage students to think critically about the physical interpretation of the results which the equation produces.

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DO - 10.1093/teamat/18.3.115

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10.1093/teamat/18.3.115