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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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