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Exploiting Symmetry in Applied and Numerical Analysis
Edited by: Eugene L. Allgower, Kurt Georg, and Rick Miranda

Lectures in Applied Mathematics
1993; 457 pp; softcover
Volume: 29
ISBN-10: 0-8218-1134-7
ISBN-13: 978-0-8218-1134-4
List Price: US$70
Member Price: US$56
Order Code: LAM/29
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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 The papers in this volume have been refereed and will not be published elsewhere.


Researchers in mathematics, physics, and engineering.

Table of Contents

  • B. Abraham-Shrauner and P. G. L. Leach -- Hidden symmetries of nonlinear ordinary differential equations
  • E. Allgower, P. Ashwin, K. Böhmer, and Z. Mei -- Liapunov-Schmidt reduction for a bifurcation problem with periodic boundary conditions on a square domain
  • E. Allgower, K. Georg, and R. Miranda -- Exploiting permutation symmetries with fixed points in linear equations
  • D. Armbruster and E. Ihrig -- Topological constraints for explicit symmetry breaking
  • P. Ashwin, K. Böhmer, and Z. Mei -- A numerical Liapunov-Schmidt method for finitely determined problems
  • N. Aubry and W. Lian -- Exploiting and detecting space-time symmetries
  • E. Barany -- Lattice periodic solutions with local gauge symmetry
  • G. Bluman -- An overview of potential symmetries
  • A. Bossavit -- On the computation of strains and stresses in symmetrical articulated structures
  • F. H. Busse and R. M. Clever -- Symmetry considerations in the numerical analysis of bifurcation sequences
  • P. Chossat and E. Protte -- On the existence of rotating waves in a steady-state bifurcation problem with \(O(3)\) symmetry
  • G. Dangelmayr, J. D. Rodriguez, and W. Güttinger -- Dynamics of waves in extended systems
  • M. Dellnitz and I. Melbourne -- The equivariant Darboux theorem
  • M. J. Englefield -- Invariant boundary conditions for the generalized diffusion equations
  • A. Fässler -- The power of the generalized Schur's lemma
  • K. Gatermann -- Computation of bifurcation graphs
  • Z. Ge -- Caustics in optimal control: An example of bifurcation when the symmetry is broken
  • K. Georg and R. Miranda -- Symmetry aspects in numerical linear algebra with applications to boundary element methods
  • M. He -- Numerical results on the zeros of Faber polynomials for \(m\)-fold symmetric domains
  • W. Hereman -- SYMMGRP.MAX and other symbolic programs for Lie symmetry analysis of partial differential equations
  • B. Hong -- A manifold solver with bifurcation and symmetry
  • B. L. Keyfitz and M. Lopes-Filho -- How to use symmetry to find models for multidimensional conservation laws
  • K. Kirchgässner and K. Lankers -- Semilinear elliptic equations in cylindrical domains--reversibility and its breaking
  • G. H. Knightly and D. Sather -- Symmetry in rotating plane Couette-Poiseuille flow
  • H.-P. Kruse, J. E. Marsden, and J. Scheurle -- On uniformly rotating fluid drops trapped between two parallel plates
  • P. J. A. J. Lambert -- The symmetry group of the integro-partial differential equations of Poisson-Vlasov
  • R. I. McLachlan -- Explicit symplectic splitting methods applied to PDE's
  • H. D. Mittelmann -- Symmetric capillary surfaces in a cube Part 2. Near the limit angle
  • D. H. Sattinger and J. S. Szmigielski -- Factorization and completely integrable systems
  • A. Steindl -- Hopf/steady-state mode interaction for a fluid conveying elastic tube with \({\mathbf D}_3\)-symmetric support
  • E. Stone and M. Kirby -- Dependence of bifurcation structures on the approximation of \(\mathrm{O}(2)\) symmetry
  • J. Tausch -- A generalization of the discrete Fourier transformation
  • E. Van Groesen -- Symmetry methods in symmetry-broken systems
  • J. Walker -- Numerical experience with exploiting symmetry groups for boundary element methods
  • Z.-Q. Wang -- On the shape of solutions for a nonlinear Neumann problem in symmetric domains
  • B. Werner -- The numerical analysis of bifurcation problems with symmetries based on bordered Jacobians
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