%0 Journal Article
%T Numerical Simulation of Diffusion Type Traffic Flow Model Using Second-Order Lax-Wendroff Scheme Based on Exponential Velocity Density Function
%A Mojammel Haque
%A Mariam Sultana
%A Laek Sazzad Andallah
%J American Journal of Computational Mathematics
%P 398-411
%@ 2161-1211
%D 2023
%I Scientific Research Publishing
%R 10.4236/ajcm.2023.133023
%X In order to control traffic congestion, many mathematical models have been used for several decades. In this paper, we study
diffusion-type traffic flow model based on exponential velocity density
relation, which
provides a
non-linear second-order parabolic partial differential equation. The analytical
solution of the diffusion-type traffic flow
model is very complicated to approximate
the initial density ![\"\"](\"Edit_e7cab758-fed3-4afd-a484-048a18c2f052.png\")
of the Cauchy problem as a function of x from
given data and it may cause a huge error. For the complexity of the analytical
solution, the numerical solution is performed by implementing an explicit upwind, explicitly centered, and
second-order Lax-Wendroff scheme for
the numerical solution. From the comparison of relative error among these three schemes, it is observed that Lax-Wendroff scheme gives less error
than the explicit upwind and explicit centered difference scheme. The
numerical, analytical analysis and comparative result discussion bring out the
fact that the Lax-Wendroff scheme with exponential velocity-density relation of
diffusion type traffic flow model is
suitable for the congested area and shows a better fit in traffic-congested region