Inverse Problems in Ordinary Differential Equations

Abstract

This thesis report includes solving the inverse problem in ordinary differential equation which is helpful in various fields. For example, we have considered a second order ordinary differential equation. In this second order ordinary differential equation, there are two types of equation. The first one is linear equation and other one is non-linear equation. In beginning, we solve the second order ordinary differential equation, then we implement the Least Square Fit Approach on linear differential equation and Newton method on non-linear differential equation to find the inverse problem. From the results, we have conclude that these methods are efficient for solving inverse problems associated with differential equations. Chapter 1 of this report describes about the inverse problem and it’s various use in many appli- cations in differential equation. Chapter 2 describes the regularization techniques for solving the inverse problems. Chapter 3 describes the various methods for solving the inverse problem in ordinary differential equation. In the end, we presented the conclusion.