## Group Theory and Numerical AnalysisThe 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 Mathematiques, Universite de Montreal (Canada). This volume has the character of a monograph and should represent a useful reference book for scientists working in this highly topical field. |

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### Contents

Symbolic Algorithms for the Painlevé Test Special Solutions and Recursion | 17 |

Continuum Limit of Lattice Approximation Schemes | 33 |

Algebraic Structures on Ordered Rooted Trees and Their Signiﬁcance to | 49 |

Aspects of Generalized DoubleBracket Flows | 65 |

Two NonLiouvillian Approaches | 91 |

Comparison of Symmetry Preserving Difference Schemes with Standard | 119 |

Symbolic Computation of Polynomials Conserved Densities Generalized | 133 |

On the Numerical Analysis of Rapid Oscillation | 149 |

On Conservation Properties of Semidiscrete Canonical Hamiltonian Equations | 165 |

Discrete Lie Symmetries for Difference Equations | 179 |

Towards a Variational Complex for the Finite Element Method | 207 |

Models of Resonantly Driven Motion of Motor Proteins in 2D Potentials | 233 |

Determination of Approximate Symmetries of Differential Equations | 249 |

Discrete and Finite Fractional Fourier Transform | 267 |

Explicit Multipoint Rational Interpolation Padé Table for Exponential | 285 |

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algorithms applied approach approximation arbitrary CEDCT coefficients commutator-free computation conservation laws constant continued fraction continuous corresponding CRM Proceedings deﬁned Deﬁnition denote densities derivative difference equations dimensional dimensions discrete symmetries E-mail address equivalent error Euler—Lagrange exact solution example exponential ﬁeld theory ﬁnal form ﬁnd ﬁnite ﬁrst ﬂows function geometric given grid Hermite polynomials highly oscillatory Hopf algebras inﬁnitesimal integration interpolation invariant involutive involutive system Iserles kinesin Krawtchouk polynomials Lagrangian lattice Lie algebra Lie group Lie symmetries linear ODE Math Mathematics Subject Classiﬁcation matrix motor protein nonlinear obtain ordinary differential equations oscillator Padé Padé approximants Painlevé equation parameter PDEs Phys polynomials potential problem projection pseudo-rigid body quadrature rank rational solutions recursion operator satisﬁes scheme Section semidiscrete singular SL(n SO(n solve space structure symbolic symplectic Theorem tion values variables variational complex vector ﬁeld zero

### Popular passages

Page 265 - Wittkopf and A. Boulton, Reduction of systems of nonlinear partial differential equations to simplified involutive forms, Eur.

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