Error analysis of exponential integrators for oscillatory second-order differential equations

@inproceedings{Grimm2006ErrorAO,
  title={Error analysis of exponential integrators for oscillatory second-order differential equations},
  author={Volker Grimm and Marlis Hochbruck},
  year={2006}
}
In this paper we analyse a family of exponential integrators for secondorder differential equations in which high-frequency oscillations in the solution are generated by a linear part. Conditions are given which guarantee that the integrators allow second-order error bounds independent of the product of the step size with the frequencies. Our convergence analysis generalises known results on the mollified impulse method by Garćıa-Archilla, Sanz-Serna and Skeel [6] and on Gautschi-type… CONTINUE READING

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References

Publications referenced by this paper.
SHOWING 1-10 OF 21 REFERENCES

Ch

  • E. Hairer
  • Lubich, and G. Wanner. Geometric Numerical…
  • 2002
Highly Influential
5 Excerpts

Numerical integration of ordinary differential equations based on trigonometric polynomials

  • W. Gautschi
  • Numer. Math., 3:381–397
  • 1961
Highly Influential
9 Excerpts

A note on the Gautschi-type method for oscillatory second-order differential equations

  • V. Grimm
  • Numer. Math., 102:61–66
  • 2005
1 Excerpt

Conservation properties of numerical integrators for highly oscillatory Hamiltonian systems

  • D. Cohen
  • Preprint, January
  • 2005

Numerical energy conservation for multi - frequency oscillatory differential equations

  • E. Hairer D. Cohen, Ch. Lubich
  • 2005

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