Phyton Implementation Of Runge -Kutta Fourth Order Algorithm: An Application To A Selected Harmonic Oscillator.

ABSTRACT

 This study is set out to use python 2.6 to implement the Runge-Kutta Fourth Order Algorithm for a selected harmonic oscillator. In order to achieve this goal a system of simple harmonic oscillator was modeled and Runge-Kutta fourth order (RK4) algorithm was used to develop a python code. The result displayed a plot of family of curves for selected values of damping factor which when compare with the known shapes of curves were the same and agreed with the laws of physics. Chapter one gives a general overview of the situation and motivation for the current work. It also defines the aim and objectives of the work. Chapter two shall present a review of literature related to the work. Special emphasis shall be given to harmonic oscillations, second order differential equations, the Runge-Kutta fourth order method (RK4) and python programming language. In chapter 3, the methods and tools employed in the work shall be presented. There shall include the model equation, the Runge-Kutta fourth order algorithms and the python code. The results from the implementation of our code shall be presented in graphs. This shall be done for different values of the damping factor, comparing the results with known results. Still in this chapter four, the results shall be interpreted. Finally, we shall present the summary and conclusion in chapter five.