ALLGOWER's Books

Introduction to Numerical Continuation Methods

By: Eugene L. Allgower,Kurt Georg

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Introduction to Numerical Continuation Methods

By: Eugene L. Allgower,Kurt Georg

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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Page Count

409

Publisher

SIAM

Published Date

ISBN 10

089871544X

ISBN 13

9780898715446

Numerical Continuation Methods

An Introduction

By: Eugene L. Allgower,Kurt Georg

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Numerical Continuation Methods

An Introduction

By: Eugene L. Allgower,Kurt Georg

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

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Page Count

402

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642612571

ISBN 13

9783642612572

Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

By: BÖHMER,ALLGOWER,GOLUBITSKY

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Bifurcation and Symmetry

Cross Influence between Mathematics and Applications

By: BÖHMER,ALLGOWER,GOLUBITSKY

Symmetry is a property which occurs throughout nature and it is therefore natural that symmetry should be considered when attempting to model nature. In many cases, these models are also nonlinear and it is the study of nonlinear symmetric models that has been the basis of much recent work. Although systematic studies of nonlinear problems may be traced back at least to the pioneering contributions of Poincare, this remains an area with challenging problems for mathematicians and scientists. Phenomena whose models exhibit both symmetry and nonlinearity lead to problems which are challenging and rich in complexity, beauty and utility. In recent years, the tools provided by group theory and representation theory have proven to be highly effective in treating nonlinear problems involving symmetry. By these means, highly complex situations may be decomposed into a number of simpler ones which are already understood or are at least easier to handle. In the realm of numerical approximations, the systematic exploitation of symmetry via group repre sentation theory is even more recent. In the hope of stimulating interaction and acquaintance with results and problems in the various fields of applications, bifurcation theory and numerical analysis, we organized the conference and workshop Bifurcation and Symmetry: Cross Influences between Mathematics and Applications during June 2-7,8-14, 1991 at the Philipps University of Marburg, Germany.

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Page Count

323

Publisher

Birkhäuser

Published Date

ISBN 10

3034875363

ISBN 13

9783034875363

Book's by ALLGOWER

Introduction to Numerical Continuation Methods

Introduction to Numerical Continuation Methods

Numerical Continuation Methods

Numerical Continuation Methods

Bifurcation and Symmetry

Bifurcation and Symmetry

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