Efficiency of fourth-order Runge-Kutta methods, Dormand Prince and Bulirsch-Stoer in solving initial value problems

Abstract

This article discusses the efficiency of the Runge-Kutta classical of fourth-order, Dormand-Prince and Bulirsch-Stoer numerical methods in solving initial value problems. The three methods were compared by solving a problem of the suspension dynamics of a vehicle when passing over a speed bump in the lane. The problem is described by a second order ordinary differential equation. Results were obtained by varying the initial step size equally for the three methods, and the behavior of the vehicle suspension in response to the speed bump height was analyzed for each step size. It was concluded that it is essential to know the nature of the problem to be solved, to properly choose the numerical method and the size of the integration step to be used. The higher the order of the integration method, the greater the possibility of using a larger step size with the desired precision. Therefore, knowledge of the nature of the problem is essential for choosing the solution method and the size of the integration step to obtain adequate results.

DOI: 10.56238/pacfdnsv1-113