Introduction to numerical continuation methods / Eugene L. Allgower, Kurt Georg.

Format:

Book

Author/Creator:

Allgower, E. L. (Eugene L.)

Contributor:

Georg, Kurt.

Society for Industrial and Applied Mathematics.

Series:

Classics in applied mathematics ; 45.

Classics in applied mathematics ; 45

Language:

English

Subjects (All):

Continuation methods.

Physical Description:

1 electronic text (xxv, 388 p. : ill.) : digital file.

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 2003.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

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. The book 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. To help potential users of numerical continuation methods create programs adapted to their particular needs, this book presents pseudo-codes and Fortran codes as illustrations. Since it first appeared, many specialized packages for treating such varied problems as bifurcation, polynomial systems, eigenvalues, economic equilibria, optimization, and the approximation of manifolds have been written. The original extensive bibliography has been updated in the SIAM Classics edition to include more recent references and several URLs so users can look for codes to suit their needs. Audience: this book continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business. A background in elementary analysis and linear algebra are adequate prerequisites for reading this book; some knowledge from a first course in numerical analysis may also be helpful.

Contents:

Introduction

The basic principles of continuation methods

Newton's method as corrector

Solving the linear systems

Convergence of Euler-Newton-like methods

Steplength adaptations for the predictor

Predictor-corrector methods using updating

Detection of bifurcation points along a curve

Calculating special points of the solution curve

Large scale problems

Numerically implementable existence proofs

PL continuation methods

PL homotopy algorithms

General PL algorithms on PL manifolds

Approximating implicitly defined manifolds

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 346-382) and index.

Description based on title page of print version.

ISBN:

0-89871-915-1

Publisher Number:

CL45 siam

CL45 SIAM