Introduction to Numerical Continuation Methods

Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.

Spis treści:
Table of Pseudo Codes
Preface to the Classics Edition
Foreword
1. Introduction
2. The Basic Principles of Continuation Methods
3. Newtons Method as Corrector
4. Solving the Linear Systems
5. Convergence of Euler-Newton-Like Methods
6. Steplength Adaptations for the Predictor
7. Predictor-Corrector Methods Using Updating
8. Detection of Bifurcation Points Along a Curve
9. Calculating Special Points of the Solution Curve
10. Large Scale Problems
11. Numerically Implementable Existence Proofs
12. PL Continuation Methods
13. PL Homotopy Algorithms
14. General PL Algorithms on PL Manifolds
15. Approximating Implicitly De¯ned Manifolds
16. Update Methods and their Numerical Stability
Appendix 1. A Simple PC Continuation Method
Appendix 2. A PL Homotopy Method
Appendix 3. A Simple Euler Newton Update Method
Appendix 4. A Continuation Algorithm for Handling Bifurcation
Appendix 5. A PL Surface Generator
Appendix 6. SCOUT | Simplicial Continuation Utilities
Bibliography
Index and Notation.