# THE ADAMS-BASHFORTH ITERATIVE SCHEME FOR INITIAL VALUE PROBLEMS

74 PAGES (12325 WORDS)
Subscribe to access this work and thousands more

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.

Cover page                                 i

Title page                                   ii

Certification                               iii

Dedication                                  iv

Acknowledgement                    v

Abstract                                      vi

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

Subscribe to access this work and thousands more
Overall Rating

5 Star
(0)
4 Star
(0)
3 Star
(0)
2 Star
(0)
1 Star
(0)
APA