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 The papers in this volume have been refereed and will not be published elsewhere.

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