Group Theory and Numerical Analysis

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Pavel Winternitz
American Mathematical Soc. - Mathematics - 298 pages
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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 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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