Technical report: mathematical modelling of Burger's equation applied in traffic flow / Shahirah Zulkifli, Nur Ilham Zainuddin and Siti Nurlina Syamimi Md Rosly

Burger's equation is a nonlinear partial differential equation occurring in various areas of applied mathematics, one of that is traffic flow. Burger's equation is the simplest equation combining both nonlinear propagation effects (uux) and diffusive effects (uxx). We interest to find the solution of inviscid and show the derivation of viscid by using Cole-Hopf transformation. In order to apply Burger's equation in traffic flow, effort will concentrate to obtain the solution. Throughout research for Burger's equation, we find the way to derive Navier-Stokes equation, to derive inviscid Burger's equation. We also show the derivation of Cole-Hopf transformation for viscid Burger's equation. Lastly, we apply any function of inviscid Burger's equation as a model traffic Flow. Beside that, we also get the solution of one-way traffic flow by using the method of linear system.