Numerical Techniques for Non-Linear Ordinary Differential Equations

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.