Numerische Mathematik

, Volume 83, Issue 3, pp 403–426 | Cite as

A Gautschi-type method for oscillatory second-order differential equations

  • Marlis Hochbruck
  • Christian Lubich
Original article

Summary.

We study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly. We prove that the method admits second-order error bounds which are independent of the product of the step size with the frequencies. Our analysis also provides new insight into the m ollified impulse method of García-Archilla, Sanz-Serna, and Skeel. We include results of numerical experiments with the sine-Gordon equation.

Mathematics Subject Classification (1991):65L05, 65L70, 65M12, 65M20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Marlis Hochbruck
    • 1
  • Christian Lubich
    • 1
  1. 1.Mathematisches Institut, Universität Tübingen, D-72076 Tübingen, Germany; e-mail: marlis@na.uni-tuebingen.de, lubich@na.uni-tuebingen.de DE

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