Solving Singularly Perturbed Higher Order Ordinary Differential Equation Using Method of Matched Asymptotic Expansion Equation

Abstract

In this thesis solution of Singularly Perturbed Higher Order Or dinary Differential Equation successfully implemented in third order singularly perturbed ordinary differential Equations. The exact solution for those equations is not easy to obtain. Hence, an analytical solution in terms of asymptotic expansion is sought. This study seeks to solve a singular perturbation in third order ordinary differential equations. Solutions to several perturbed or dinary differential equations are obtained in terms of asymptotic expansion. Mathematica 12 soft ware computer algebra system is used to perform the detail algebraic computations. The results of analytical solution are illustrated by graphs using selected pa rameters solutions separately. Hence, the exact solution obtained using Method of Matched Asymptotic Expansion (MMAE) are compared by plotting the graph to show their accuracy. MMAE is one of the best methods to solve exact solution of singular per-turbation problems in third order ordinary differential equation.