Variations Iteration Method for Solving Delay Differential Equation/Numerical Analysis

ABSTRACT   

A  powerful  and  effective  numerical  tool  called  the  Variational  Iteration Method  has  been  used  to  solve  various  kinds  of  differential  equations  over  the years. Though the Variational Iteration Method has not been used solely to solve various  kinds  of  differential  equations  as  it  has  always  been  coupled  with polynomials/transforms. The core of this project is centred on using basically the Variational Iteration Method in solving Delay Differential Equation of First and Second Order. With a very few number of iterations, we obtain an approximated series solution which converges to the exact solution.

TABLE OF CONTENTS 

COVER PAGE                  i 

TITLE PAGE                  ii 

CERTIFICATION                  iii  

DEDICATION                  iv  

ACKNOWLEDGEMENT               v 

TABLE OF CONTENTS                vi 

ABSTRACT                   viii 

CHAPTER ONE: INTRODUCTION 

1.1 Background of the Study              1   

1.2 Objectives of the Study               7   

1.3 Scope of the Study                7 

1.4 Significance of the Study              7   

CHAPTER TWO: BASIC DEFINITIONS AND CONCEPTS 

2.1 Introduction to Differential Equations          9   

2.2 Functional Differential Equations            14 

2.3 Introduction to Delay Differential Equations         15 

2.4 Time-Delay Systems                23 

CHAPTER  THREE:  VARIATIONAL  ITERATION  METHOD  FOR SOLVING DELAY DIFFERENTIAL EQUATIONS 

3.1 Introduction to new nomenclatures            27   

3.2 Variational Iteration Method (VIM)            32   

3.3 Modified Variational Iteration Method (MVIM)        38   

3.4  Convergence of Variational Iteration Method for Second-Order Delay Differential Equations              40   

CHAPTER FOUR: APPLICATIONS 

4.1 Delay Differential Equation              45 

4.2 Population Dynamics                50 

CHAPTER FIVE: SUMMARY AND CONCLUSION 

5.1 Summary                   55 

5.2 Conclusion                  56 

Bibliography                   57