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