Error growth in the numerical integration of periodic orbits

M. Calvo, M.P. Laburta, J.I. Montijano and L. Rández

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 12, 2646-2661

Abstract: This paper is concerned with the long term behaviour of the error generated by one step methods in the numerical integration of periodic flows. Assuming numerical methods where the global error possesses an asymptotic expansion and a periodic flow with the period depending smoothly on the starting point, some conditions that ensure an asymptotically linear growth of the error with the number of periods are given. A study of the error growth of first integrals is also carried out. The error behaviour of Runge–Kutta methods implemented with fixed or variable step size with a smooth step size function, with a projection technique on the invariants of the problem is considered.

Keywords: Geometric integration; Runge–Kutta methods; Invariant preservation; Long-time integration (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:12:p:2646-2661

DOI: 10.1016/j.matcom.2011.05.007

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