A fluid dynamic traffic flow model based on a non-linear velocity-density function is considered. The model provides a quasi-linear first order hyperbolic partial differential equation which is appended with initial and boundary data and turns out an initial boundary value problem (IBVP). A first order explicit finite difference scheme of the IBVP known as Lax-Friedrich's scheme for our model is presented and a well-posedness and stability condition of the scheme is established. The numerical scheme is implemented in order to perform the numerical features of error estimation and rate of convergence. Fundamental diagram, density, velocity and flux profiles are presented.

A second order fluid dynamical traffic flow model is considered which is a parabolic type second order partial differential equation appended with initial and boundary conditions reads as an initial boundary value problem (IBVP). For a linear velocity-density relation the paper presents the analytical solution of the model by using Cole-Hopf transformation. For the numerical solution of the IBVP, we investigate explicit central difference scheme and implement the numerical scheme by developing computer programming code. Error estimation is produced which shows the numerical solution is accurate up to eight decimal places and this result is much better than the work presented in [6]. The numerical feature of rate of convergence observed by graphical presentation is also found better than the previous work. The computed numerical simulation results are seen in a good qualitative agreement with the well known traffic flow behavior for various parameters.