Numerische Mathematik

, Volume 83, Issue 3, pp 403–426

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

  • Marlis Hochbruck
  • Christian Lubich
Original article

DOI: 10.1007/s002110050456

Cite this article as:
Hochbruck, M. & Lubich, C. Numer. Math. (1999) 83: 403. doi:10.1007/s002110050456


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 

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:, DE

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