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Abstract: This paper gives examples of how computer algebra systems can help us to understand nonlinear dynamical systems and their numerical simulations. We caution against naive use of exact arithmetic, but we give examples where elementary use is helpful. We also look at the use of polynomial computations---such as factoring, computation of discriminants, and Grobner bases---in bifurcation studies. 1 Introduction This paper investigates the role symbolic computation can play in the... (Update)
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BibTeX entry: (Update)
@misc{ corless-symbolic,
author = "Robert M. Corless",
title = "Symbolic Computation in Nonlinear Dynamics",
url = "citeseer.ist.psu.edu/341091.html" }
Citations (may not include all citations):204 Methods and Applications of Interval Analysis (context) - Moore - 1979
176 An Introduction to Chaotic Dynamical Systems (context) - Devaney - 1989
44 Handbook of Integer Sequences (context) - Sloane
17 Numerical Methods for Dynamical Systems (context) - Beyn - 1991
14 the scope of the Method of Modified Equations (context) - Griffiths, Sanz-Serna - 1986
10 Solving Problems in Scientific Computing using Maple and MAT.. (context) - Gander, Hrebi'icek - 1993
6 Error Backward (context) - Corless - 1993
5 Sur l'Inversion et l'It'eration Continue des S'eries Formell.. (context) - Labelle - 1980
4 Computers and Mathematics (context) - Kaltofen, Watt - 1989
3 personal communication (context) - Briggs
3 Computer Aided Proofs in Analysis (context) - Meyer, Schmidt - 1991
2 Maple share library (context) - Corless - 1990
2 Symbolic Computation in Fluid Mechanics and Heat Transfer (context) - Bau, Herbert et al. - 1988
2 Applied Mathematical Sciences (context) - Rand, Armbruster et al. - 1987
2 and Fractals (context) - McCauley, Dynamics - 1993
1 Springer-Verlag Problem Books in Mathematics (context) - Barbeau - 1989
1 Symbolic Computation and Perturbation Methods Using Elliptic.. (context) - Coppola, Rand - 1989
1 Bifurcation in a flow-induced vibration model (context) - Corless
1 What good are numerical solutions of chaotic differential eq.. (context) - Corless
1 Shadowing and Iterative Interpolation for Cebysev Mixing Tra.. (context) - Gavelek, Erber - 1992
1 A problem in automatic control (context) - Katende, Jutan et al.
1 Mathematical Computation with Maple V: Ideas and Application.. (context) - Lee - 1993
1 personal communication (context) - Salvy
1 Chaos and Continued Fractions (context) - Corless, Frank et al. - 1990
1 Springer-Verlag to appear (context) - Corless, Recipes - 1994
1 Continued Fractions (context) - Khintchin - 1963
1 Nonlinear Sequence Transformations for the Acceleration of C.. (context) - Weniger - 1989
1 Continued Fractions and Chaos (context) - Corless - 1992
Documents on the same site (http://www.apmaths.uwo.ca/~rcorless/papers/symbolic/index.html): More
Editor's Corner: Cofactor Iteration - Corless (1996) (Correct)
The Symbolic Generation of Finite-Difference Formulas - Jacek Rokicki (Correct)
What is a solution of an ODE? - Corless (1993) (Correct)
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