ABSTRACT
In this project work, we studied the Adams-Bashforth scheme for solving initial value problems. We gave an indebt explanation on the Adam-Bashforth scheme, its consistency, stability, and convergence, the two and three step methods were also derived. Numerical solutions were obtained using four (4) examples.
TABLE OF CONTENTS
Cover page i
Title page ii
Certification iii
Dedication iv
Acknowledgement v
Abstract vi
Table of contents vii
CHAPTER ONE: INTRODUCTION
1.1. Background of Study 1
1.2. Objectives Of The Study 10
1.3. Scope of the Study 11
1.4. Significance of the Study 12
CHAPTER TWO: BASIC CONCEPTS AND DEFINITIONS
2.1. Differential Equation 13
2.2. Ordinary Differential Equation 14
2.3. Initial Value Problems 15
2.4. Iteration 16
2.5. Numerical Method 16
2.6. Mesh Points 17
2.7. Local Truncation Error or Discretization Error 18
2.8. Single and Multi-Step Method 18
2.8.1. Single Step Methods 18
2.8.2. Multi-Step Methods 26
2.9. Order Of A Method 28
2.10. Predictor-Corrector Methods 28
2.11. Interval of Validity 30
2.12. Solution 30
2.13. Existence and Uniqueness of An Initial Value Problem 30
2.14. Mean Value Theorem 31
CHAPTER THREE: ADAM-BASHFORTH LINEAR MULTI-STEP ITERATIVE SCHEME FOR INITIAL VALUE PROBLEMS
3.1. The Adam-Bashforth Iterative Scheme 32
3.2. Derivation, Order and Truncation Error of the Adam Bashforth Iterative Scheme 33
3.3. Consistency, Stability and Convergence of Linear Multi-Step Methods 41
CHAPTER FOUR: NUMERICAL EXPERIMENTS OF THE ADAM-BASHFORTH METHOD 49
CHAPTER FIVE: SUMMARY AND CONCLUSION
5.1. Summary 61
5.2. Conclusion 61
BIBLOGRAPHY