The Contraction Mapping Principle (UMAP)

This module studies the Picard technique for estimating solutions of equations. The technique includes an iterative process, i.e., an algorithm, that can be understood and interpreted with ease pictorally and be implemented readily on inexpensive and widely-available calculators. The unit applies the technique to solve a wide variety of physical problems.

Table of Contents:

1. INTRODUCTION

2. THE PROBLEM

3. THE ALGORITHM
3.1 Example 1
3.2 Example 2
3.3 Example 3

4. CONTRACTION MAPPINGS
4.1 Example 4
4.2 Example 5
4.3 Example 6
4.4 Example 7
4.5 Example 8

5. FURTHER EXAMPLES AND APPLICATIONS
5.1 Example 9
5.2 Example 10
5.3 Example 11

6. RELATED NUMERICAL METHODS

7. NUMERICAL ANALYSIS

8. MODEL EXAM

9. ANSWERS TO EXERCISES

10. SOLUTIONS FOR MODEL EXAM

11. APPENDIX