Error growth in the numerical integration of periodic orbits
Error growth in the numerical integration of periodic orbits
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DOI：
10.1016/j.matcom.2011.05.007
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
M. Calvo;M. P. Laburta;J. I. Montijano;L. Rández
中科院分区：
文献类型：
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作者：
M. Calvo;M. P. Laburta;J. I. Montijano;L. Rández
本文研究了周期流数值积分中一步法产生的误差的长期行为。假设数值方法的全局误差具有渐近展开和周期流的周期光滑依赖于起始点，一些条件，确保渐近线性增长的误差的周期数。首次积分的误差增长的研究也进行了。龙格-库塔方法的误差行为被认为是固定或可变步长与光滑步长函数，与投影技术的不变量的问题。
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.