Numerical dynamics of ordinary differential equations with singularity

Author:
Kevin Hockett

Journal:
Proc. Amer. Math. Soc. **117** (1993), 369-379

MSC:
Primary 58F13; Secondary 34A50, 34C99, 65L99

MathSciNet review:
1107272

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Abstract: We investigate the global dynamics of Euler's method and second order Runge-Kutta when applied to certain nonlinear ordinary differential equations that possess a singularity. We show that the numerics admit spurious `chaotic' dynamics in the form of subshifts of finite type with positive topological entropy *independent* of the choice of stepsize. We show that using a higher order method can, in fact, *increase* the topological entropy of the numerical dynamics. Techniques from complex analytic dynamics give some insight into this phenomenon.

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1107272-5

Article copyright:
© Copyright 1993
American Mathematical Society