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Introduction to Numerical Continuation Methods: Classics in Applied Mathematics, cartea 45

Autor Eugene L. Allgower, Kurt Georg
en Limba Engleză Paperback – 31 dec 1986
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.
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Specificații

ISBN-13: 9780898715446
ISBN-10: 089871544X
Pagini: 414
Dimensiuni: 177 x 254 x 19 mm
Greutate: 0.73 kg
Editura: Society for Industrial and Applied Mathematics
Colecția Society for Industrial and Applied Mathematics
Seria Classics in Applied Mathematics

Locul publicării:Philadelphia, United States

Cuprins

Table of Pseudo Codes; Preface to the Classics Edition; Foreword; 1. Introduction; 2. The Basic Principles of Continuation Methods; 3. Newton's 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.

Descriere

Describes numerical continuation methods that have provided important contributions toward the numerical solution of nonlinear systems.