Abstract:
This thesis provides the development of families of Runge Kutta methods up to 4th
order for solving non-linear ordinary differential equations. Our motive is to deeply
study and compare several third and fourth order Runge Kutta methods for the sake
of error analysis. First, the basics of differential equations and numerical methods
are elaborated along with development of a few elementary methods. Subsequently,
second and third order Runge Kutta methods are developed from a general framework.
The comparison of several third order Runge Kutta methods applied to a few
non-linear problems is provided. Endmost, development and comparisons of several
fourth order Runge Kutta methods applied to a bunch of non-linear problems are
provided.
