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Orbits Worth Betting On

Rob Knapp
Organization: Wolfram Research, Inc.
Department: Kernel Technology
Stan Wagon
Organization: Macalester College
Department: Department of Mathematics and Computer Science
URL: http://www.stanwagon.com/

This article examines how one can compute accurate orbits to systems of ODE's which are sensitive to initial conditions. The Duffing equation is used as an example to show how inaccurate orbits can be detected, their cause (discussed in terms of the Lyapunov characteristic exponent), and a method that can be used to compute accurate orbits.

*Mathematics > Calculus and Analysis > Differential Equations
*Wolfram Technology > Kernel > Numerics

orbits, ordinary differential equations, Duffing equation, Lyapunov characteristic exponent
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Orbits.nb (278.2 KB) - Mathematica Notebook

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Orbits.ma (251.9 KB) - Mathematica Notebook 2.2 or older