Gizaw, Solomon (PhD)Murad, Ayana2021-08-052023-11-182021-08-052023-11-182021-04-26http://etd.aau.edu.et/handle/12345678/27604Transportation has a major contribution in the development of the human civilization. The accessibility of highway transportation has given many focal points that contribute to a high standard of living. However, many issues related to the highway mode of transportation exist. These issues incorporate highway related accidents, parking troubles, clog, natural risks (carbon emissions, clamor contamination, etc.) and delay. To solve these problems building expressways is one of the solutions. Even though building express way is a good solution for solving problems related to highway traffic, Data collected from Ethiopia Toll Road Enterprise indicated that, on average, about 417 road crashes were reported since September 2014 to February 2016 that leads around 672 traffic accidents. Road traffic crashes (RTCs) are globally acknowledged as increasing threat to society, because they can affect many lives when they result in severe injury or fatality. Ethiopia is among the leading countries in road traffic accident. The recent road safety record of Addis Ababa- Adama expressway is also alarming the severity of the situation and calling for an integral effort of all pertinent stakeholders to reverse the trend. In this research we modeled traffic crashes and traffic volumes in Addis – Adama express way with ordinary differential equation using interpolation methods (i.e. newton DVD and Lagrange interpolations). We solved the ordinary differential equations we got after modeling using Euler method and Runge – Kutta method. We observed if there is any relation between traffic crash and traffic volume. We analyzed the traffic crash data parameters i.e. vehicle type, vehicle type with weekdays and direction to observe the factors causing traffic accident. The data we used for modelling and analyzing is collected from ETRE. Using the mathematical model of traffic crash, we were able to predict 2020 number of traffic crash. The finding shows that traffic crash and traffic volume have linear relationship. From the analysis we observed that Small automobiles are causing the highest traffic crash, the highest number of traffic crash occurred in Friday, and vehicles heading to mojo are causing the highest number of traffic crash. Therefore, ETRE should take restrict monitoring on small automobiles, vehicles heading to mojo, and in weekends.enComputational ModelingNumerical AnalysisInterpolationNewton Divided DifferenceLagrange InterpolationsEuler MethodRunge Kutta MethodOdeThesis