Parcialne diferencialne enačbe in pretok prometa

Puntar, Janez (author), Slapar, Marko (mentor)

V magistrskem delu bomo analizirali gibanje vozil na enopasovni cesti s pomočjo matematičnega modela. Model prometa bo temeljil na dveh količinah: hitrostnem polju in gostoti prometa. S pomočjo ohranitvenega zakona bomo izpeljali prometno enačbo. Prometna enačba je kvazilinearna parcialna diferencialna enačba dveh spremenljivk, ki jo lahko rešujemo s pomočjo metode karakteristik. V zadnjem delu bomo konkretno obravnavali nekatere prometne situacije.

• Language: Slovenian
• Keywords: sistemi diferencialnih enačb
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: PEF - Faculty of Education
• Year: 2020
• PID: 20.500.12556/RUL-118189
• COBISS.SI-ID: 25916931
• Publication date in RUL: 03.09.2020

Secondary language

• Language: English
• Title: Partial differential equations and traffic flow

Abstract

In this masters thesis we analyze the movement of vehicles on a one lane road using a mathematical model. Our traffic model will depend on two quantities: velocity field and traffic density. Using a conservation law, we derive the traffic equation. The traffic equation is a quasilinear partial differential equation that we can solve using the method of characteristics. In the last part of the thesis, we study a few examples of different traffic situations.

• Keywords: systems of diferential equations