This book studies the numerical analysis of the system of six coupled nonlinear Ordinary Differential Equations (ODEs) which are aroused in the reduction of stratified Boussinesq Equation. This book aims to introduce the several methods of solving coupled differential equations, which occur rather frequently in the study of stratified Boussinesq equations. This book also includes the unique ways of solving coupled ODEs by Modified Euler Method, Runge-Kutta fourth order method and Adomian Decomposition Method which was originally introduced the author by himself.