A Stroboscopic Numerical Method for Highly Oscillatory Problems

Maripaz Calvo (1) , Philippe Chartier (2) , Ander Murua (3) , Jesus Maria Sanz-Serna (1)

1 MA - Departamento de Matemática Aplicada [Valladolid]
2 IPSO - Invariant Preserving SOlvers
3 Konputazio Zientziak eta A.A. Saila [Spain]

We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging. The technique may be easily implemented in combination with standard software and may be applied with variable step sizes. Numerical experiments show that the suggested algorithms may be substantially more efficient than standard numerical integrators.

Domaines: Analyse numérique [math.NA]

Maripaz Calvo, Philippe Chartier, Ander Murua, Jesus Maria Sanz-Serna. A Stroboscopic Numerical Method for Highly Oscillatory Problems. Engquist Björn, Runborg Olof, Tsai Yen-Hsi R. Numerical analysis of multiscale computations: proceedings of a winter workshop at the Banff International Research Station 2009, 82, Springer, pp.71-85, 2012, 978-3-642-21942-9. ⟨10.1007/978-3-642-21943-6⟩. ⟨hal-00777182⟩