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Exploiting Symmetry in Applied and Numerical Analysis

Author: Eugene L. Allgower

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 457

ISBN-13: 9780821811344

Symmetry plays an important role in theoretical physics, applied analysis, classical differential equations, and bifurcation theory. Although numerical analysis has incorporated aspects of symmetry on an ad hoc basis, there is now a growing collection of numerical analysts who are currently attempting to use symmetry groups and representation theory as fundamental tools in their work. This book contains the proceedings of an AMS-SIAM Summer Seminar in Applied Mathematics, held in 1992 at Colorado State University. The seminar, which drew about 100 scientists from around the world, was intended to stimulate the systematic incorporation of symmetry and group theoretical concepts into numerical methods. The papers in this volume have been refereed and will not be published elsewhere.

Exploiting Symmetry in Applied and Numerical Analysis

Author: Eugene L. Allgower

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 476

ISBN-13: 9780821896976

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Numerical Bifurcation Analysis for Reaction-Diffusion Equations

Author: Zhen Mei

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 422

ISBN-13: 3662041774

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This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

New Developments in Difference Equations and Applications

Author: SuiSun Cheng

Publisher: Routledge

Published: 2017-09-29

Total Pages: 382

ISBN-13: 1351428802

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The late Professor Ming-Po Chen was instrumental in making the Third International Conference on Difference Equations a great success. Dedicated to his memory, these proceedings feature papers presented by many of the most prominent mathematicians in the field. It is a comprehensive collection of the latest developments in topics including stability theory, combinatorics, asymptotics, partial difference equations, as well as applications to biological, social, and natural sciences. This volume is an indispensable reference for academic and applied mathematicians, theoretical physicists, systems engineers, and computer and information scientists.

Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems

Author: Bernold Fiedler

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 816

ISBN-13: 3642565891

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Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.

Numerical Methods for Bifurcations of Dynamical Equilibria

Author: Willy J. F. Govaerts

Publisher: SIAM

Published: 2000-01-01

Total Pages: 384

ISBN-13: 9780898719543

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Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

CRC Handbook of Lie Group Analysis of Differential Equations

Author: Nail H. Ibragimov

Publisher: CRC Press

Published: 1995-10-24

Total Pages: 572

ISBN-13: 9780849394195

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Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Introduction to Numerical Continuation Methods

Author: Eugene L. Allgower

Publisher: SIAM

Published: 2003-01-01

Total Pages: 409

ISBN-13: 089871544X

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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.

Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics

Author: N.H. Ibragimov

Publisher: Springer Science & Business Media

Published: 2011-06-27

Total Pages: 379

ISBN-13: 9401120501

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On the occasion of the 150th anniversary of Sophus Lie, an International Work shop "Modern Group Analysis: advanced analytical and computational methods in mathematical physics" has been organized in Acireale (Catania, Sicily, October 27 31, 1992). The Workshop was aimed to enlighten the present state ofthis rapidly expanding branch of applied mathematics. Main topics of the Conference were: • classical Lie groups applied for constructing invariant solutions and conservation laws; • conditional (partial) symmetries; • Backlund transformations; • approximate symmetries; • group analysis of finite-difference equations; • problems of group classification; • software packages in group analysis. The success of the Workshop was due to the participation of many experts in Group Analysis from different countries. This book consists of selected papers presented at the Workshop. We would like to thank the Scientific Committee for the generous support of recommending invited lectures and selecting the papers for this volume, as well as the members of the Organizing Committee for their help. The Workshop was made possible by the financial support of several sponsors that are listed below. It is also a pleasure to thank our colleague Enrico Gregorio for his invaluable help of this volume.

Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems

Author: Eusebius Doedel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 482

ISBN-13: 1461212081

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The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.