Mark McCartney. 2004. Keep your distance! using second-order ordinary differential equations to model traffic flow. International Journal of Mathematical Education in Science and Technology. 35(4): 588-596,
Article Abstract: A simple mathematical model for how vehicles follow each other along a stretch of road is presented. The resulting linear second-order differential equation with constant coefficients is solved and interpreted. The model can be used as an application of solution techniques taught at ﬁrst-year undergraduate level and as a motivator to encourage students to think critically about the physical interpretation of the results which such equations produce.
Usually partial differential equations are used to model traffic flow, but this paper uses a set of ordinary differential equations to model the traffic flow. Moreover, the author provides a set of exercises for students.
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