• Dr.S. NARESH KUMAR
• ABIRAMI.K
• SELVA NANDHINI.N

The Runge –Kutta method is a technique of numerically iterating Ordinary Differential Equations (ODE). Nowadays the need for solving real-world problems has been increased. The problem in question here is a traffic flow problem involving different parameters. Solving vehicular traffic flows based on Partial Differential Equations (PDE) are more complicated and time-consuming that cannot be done in real-time, so ODE mathematical models are constructed from obtained PDE. The accuracy of the Runge-Kutta method is more reliable compared to other iteration methods. These accurate solutions can be widely used to solve the increasing need for traffic flow optimization. In this paper, the construction of an ODE mathematical model is done for a real-world problem, in particular, traffic flow is discussed and a numerical solution is given as an example. We have also compared the solution obtained from the RK method with Euler's method, thus showing, the solution obtained from an IV ORDER Runge-Kutta method (for first order ODE) is more accurate.

Runge-Kutta method, Ordinary differential equation, Traffic flow, Partial Differential Equations, Mathematical models

"A STUDY ON APPLICATION OF RUNGE- KUTTA METHOD WITH RESPECT TO TRAFFIC FLOW PROBLEM", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 6, page no.121-126, June 2019, Available :http://www.jetir.org/papers/JETIR1907774.pdf

"A STUDY ON APPLICATION OF RUNGE- KUTTA METHOD WITH RESPECT TO TRAFFIC FLOW PROBLEM", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 6, page no. pp121-126, June 2019, Available at : http://www.jetir.org/papers/JETIR1907774.pdf