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Orbits Worth Betting On
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| Organization: | Wolfram Research, Inc. |
| Department: | Kernel Technology |
| Organization: | Macalester College |
| Department: | Department of Mathematics and Computer Science |
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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.
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orbits, ordinary differential equations, Duffing equation, Lyapunov characteristic exponent
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| Orbits.nb (278.2 KB) - Mathematica Notebook |
Files specific to Mathematica 2.2 version:
| | Orbits.ma (251.9 KB) - Mathematica Notebook 2.2 or older |
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