Numerical dynamics of ordinary differential equations with singularity

Hockett, Kevin

doi:10.1090/S0002-9939-1993-1107272-5

Numerical dynamics of ordinary differential equations with singularity
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Proc. Amer. Math. Soc. 117 (1993), 369-379 Request permission

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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