Volker Grimm and Marlis Hochbruck 2006 J. Phys. A: Math. Gen. 39 5495 doi:10.1088/0305-4470/39/19/S10
Volker Grimm and Marlis Hochbruck
Show affiliationsIn this paper, we analyse a family of exponential integrators for second-order 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 generalizes known results on the mollified impulse method by García-Archilla, Sanz-Serna and Skeel (1998, SIAM J. Sci. Comput. 30 930–63) and on Gautschi-type exponential integrators (Hairer E, Lubich Ch and Wanner G 2002 Geometric Numerical Integration (Berlin: Springer), Hochbruck M and Lubich Ch 1999 Numer. Math. 83 403–26).
02.60.Lj Ordinary and partial differential equations; boundary value problems
Issue 19 (12 May 2006)
Received 16 September 2005, in final form 11 December 2005
Published 24 April 2006
Volker Grimm and Marlis Hochbruck 2006 J. Phys. A: Math. Gen. 39 5495
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