Honors College Thesis

 

Solveig T.Numerical Method and Step Size Variation in the Lorenz Equations Public

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  • The relative accuracy of solutions to chaotic systems was examined using the Lorenz system as a case study. The classical fourth order Runge-Kutta method was employed to generate solutions using various step sizes, and the resultant solutions were compared. A second set of solutions was then computed using one of the second order Runge-Kutta methods and the same range of step sizes as before. The resultant data suggest that shortterm accuracy can be significantly increased by decreasing the step size of the numerical method, and a more accurate method similarly increases short-term accuracy. As expected, the long-term solutions eventually diverge; the qualitative behavior of these long-term solutions is still evident regardless of the step size or the method used.
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