Lectures in Applied Mathematics 1993; 457 pp; softcover Volume: 29 ISBN10: 0821811347 ISBN13: 9780821811344 List Price: US$74 Member Price: US$59.20 Order Code: LAM/29
 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 AMSSIAM 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 The papers in this volume have been refereed and will not be published elsewhere. Readership Researchers in mathematics, physics, and engineering. Table of Contents  B. AbrahamShrauner and P. G. L. Leach  Hidden symmetries of nonlinear ordinary differential equations
 E. Allgower, P. Ashwin, K. Böhmer, and Z. Mei  LiapunovSchmidt 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 LiapunovSchmidt method for finitely determined problems
 N. Aubry and W. Lian  Exploiting and detecting spacetime 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 steadystate 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. LopesFilho  How to use symmetry to find models for multidimensional conservation laws
 K. Kirchgässner and K. Lankers  Semilinear elliptic equations in cylindrical domainsreversibility and its breaking
 G. H. Knightly and D. Sather  Symmetry in rotating plane CouettePoiseuille 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 integropartial differential equations of PoissonVlasov
 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/steadystate 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 symmetrybroken 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
