Simulasi Numerik Model Matematika Arus Lalu Lintas Berbasis Fungsi Velositas Underwood - Dian Firmayasari; Muh. Isbar Pratama; Nur Ahyaniyanti Rasyid; Harianto (Jurusan Matematika FMIPA UNM, 2021)
Abstract. Mathematical traffic flow model was first developed by Lighthill, Whitham and Richards in 1956, known as (LWR) model. In LWR model, velocity function was most important. In this paper, Underwood velocity function was used. Implicit finite difference method used to found the numerical solution of LWR model with Underwood velocity model. Convergence the implicit finite difference method proved using the Lax equivalence theorem. The numerical simulation of 10 km highway of single lane was performed for 1 hours using the implicit finite difference method based on artificially generated initial and boundary data. Numerical simulation performed with two different parameters. An experimental result for the stability condition of the numerical scheme was also presented. Density, velocity, and fluks for 1 hours was experimental result of numerical simulation.