Abstract:
In this report we discussed dbout methods of Runge-Kutta in arbitrary second and fourth order ordinary
differential equations and system of first order ordinary differential equations with its application. The
report is divided in to three chapters; the first chapter includes introduction and preliminaries which are
used for our subsequent discussion of the next two chapters. In the second chapter; the derivation of
second order Runge-Kutta formulas, higher order Runge-Kuutta formulas, second order differential
equations are discussed thoroughly; And in the third chapter; some applications of Runge-Kutta Methods
are discussed. Runge-Kutta methods have many applications including the numerical solution of the non
linear pendulum and impulsive forces. In this report, the non linear damped pendulum and impulsive
force equation has been solved using Runge-Kutta methods.
