A new family of Runge–Kutta type methods for the numerical integration of perturbed oscillators

@article{Gonzlez1999ANF,
  title={A new family of Runge–Kutta type methods for the numerical integration of perturbed oscillators},
  author={Ana B. Gonz{\'a}lez and Pablo Mart{\'i}n and Jos{\'e}-Miguel Farto},
  journal={Numerische Mathematik},
  year={1999},
  volume={82},
  pages={635-646}
}
Summary. Our task in this paper is to present a new family of methods of the Runge–Kutta type for the numerical integration of perturbed oscillators. The key property is that those algorithms are able to integrate exactly, without truncation error, harmonic oscillators, and that, for perturbed problems the local error contains the perturbation parameter as a factor. Some numerical examples show the excellent behaviour when they compete with Runge–Kutta–Nyström type methods. 

Figures and Topics from this paper.

References

Publications referenced by this paper.
SHOWING 1-9 OF 9 REFERENCES

The development of variable–step size symplectic integrators, with application to the two–body problem

M. P. Calvo, J. M. Sanz–Serna
  • SIAM J. Sci. Comput
  • 1993
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

An algorithm for the systematic construction of solutions to perturbed problems

J. M. Farto, A. B. González
  • Computer Physics Communications

Similar Papers