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Group Theory and Numerical Analysis
Edited by: P. Winternitz, Université de Montréal, QC, Canada, D. Gomez-Ullate, Universitat Politècnica de Catalunya, Barcelona, Spain, A. Iserles, University of Cambridge, UK, D. Levi, Università degli Studi Roma, Italy, P. J. Olver, University of Minnesota, Minneapolis, MN, R. Quispel, La Trobe University, Victoria, Australia, and P. Tempesta, Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
2005; 298 pp; softcover
Volume: 39
ISBN-10: 0-8218-3565-3
ISBN-13: 978-0-8218-3565-4
List Price: US$109
Member Price: US$87.20
Order Code: CRMP/39
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The Workshop on Group Theory and Numerical Analysis brought together scientists working in several different but related areas. The unifying theme was the application of group theory and geometrical methods to the solution of differential and difference equations. The emphasis was on the combination of analytical and numerical methods and also the use of symbolic computation. This meeting was organized under the auspices of the Centre de Recherches Mathématiques, Université de Montréal (Canada).

This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students, research mathematicians, physicists, and engineers interested in analytical and numerical solutions of ordinary differential equations and partial differential equations.

Table of Contents

  • A. M. Atoyan and J. Patera -- Continuous extension of the discrete cosine transform, and its applications to data processing
  • D. Baldwin, W. Hereman, and J. Sayers -- Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs
  • C. M. Bender -- Continuum limit of lattice approximation schemes
  • H. Berland and B. Owren -- Algebraic structures on ordered rooted trees and their significance to Lie group integrators
  • A. M. Bloch and A. Iserles -- Aspects of generalized double-bracket flows
  • E. Celledoni -- Eulerian and semi-Lagrangian schemes based on commutator-free exponential integrators
  • E. S. Cheb-Terrab -- Second order linear ODEs: Two non-Liouvillian approaches
  • P. A. Clarkson -- On rational solutions of the fourth Painlevé equation and its Hamiltonian
  • C. Cyr-Gagnon -- Comparison of symmetry preserving difference schemes with standard numerical methods
  • W. Hereman, J. A. Sanders, J. Sayers, and J. P. Wang -- Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations
  • A. Iserles -- On the numerical analysis of rapid oscillation
  • R. Kozlov -- On conservation properties of semidiscrete canonical Hamiltonian equations
  • D. Levi and M. A. Rodríguez -- Discrete Lie symmetries for difference equations
  • D. Lewis -- Trivializations, factorizations, and geometric integration for pseudo-rigid bodies
  • E. L. Mansfield and G. R. W. Quispel -- Towards a variational complex for the finite element method
  • J. Middleton and J. A. Tuszynski -- Models of resonantly driven motion of motor proteins in 2D potentials
  • J. Bonasia, F. Lemaire, G. Reid, R. Scott, and L. Zhi -- Determination of approximate symmetries of differential equations
  • K. B. Wolf -- Discrete and finite fractional Fourier transform
  • W. J. Zakrzewski -- Some nanotube-like systems and their discrete equations
  • A. Zhedanov -- Explicit multipoint rational interpolation Padé table for exponential and power functions
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