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Error growth in the numerical integration of periodic orbits

Author

Listed:
  • Calvo, M.
  • Laburta, M.P.
  • Montijano, J.I.
  • Rández, L.

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.

Suggested Citation

  • Calvo, M. & Laburta, M.P. & Montijano, J.I. & Rández, L., 2011. "Error growth in the numerical integration of periodic orbits," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(12), pages 2646-2661.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:12:p:2646-2661
    DOI: 10.1016/j.matcom.2011.05.007
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    Cited by:

    1. Hendrik Ranocha & Manuel Quezada Luna & David I. Ketcheson, 2021. "On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-26, December.

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