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On the Use of the Gautschi-Type Exponential Integrator for Wave Equations

In: Numerical Mathematics and Advanced Applications

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  • Volker Grimm

    (Heinrich-Heine-Universität, Mathematisches Institut, Lehrstuhl für Angewandte Mathematik, Universitätsstraσe 1)

Abstract

Wave equations are especially challenging for numerical integratorss since the solution is often not smooth and there is no smoothing in time. The largest usable step size of standard integrators, as for example the often used Störmer- Verlet-Leap-Frog-scheme, depends on the space discretisation. The better the approximation in space, the smaller the required step size of the integrator. The presented exponential integrator allows for error bounds independent of the space discretisation but only dependent on constants arising from the original problem. This favourable property is demonstrated with the Sine-Gordon equation.

Suggested Citation

  • Volker Grimm, 2006. "On the Use of the Gautschi-Type Exponential Integrator for Wave Equations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 557-563, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_52
    DOI: 10.1007/978-3-540-34288-5_52
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