On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations

Numerische Mathematik

Volumn 100, Issue 1, 2005, Pages 71-89

  Grimm, Volker ^a  

^a LA TROBE UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 15544380884     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-005-0583-8     Document Type: Article

References (14)

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4. Grimm, V.: Exponentielle Integratoren als Lange-Zeitschritt-Verfahren für oszillatorische Differentialgleichungen zweiter Ordnung, PhD thesis, Mathematisches Institut, Universität Düsseldorf, Germany, 2002
5. Grubmüller, H. : Dynamiksimulation sehr großer Makromoleküle auf einem Parallelrechner, PhD thesis, Physik-Dept. der Tech. Univ. München, 1994
6. Hairer, E., Lubich, C.: Long-time energy conservation of numerical methods for oscillatory differential equations. SIAM J. Numer. Anal. 38, 414-441 (2000)
7. Hairer, E., Lubich, Ch., Wanner, G.: Geometric Numerical Integration. Springer-Verlag, 2002
8. Hochbruck, M., Lubich, Ch.: A Bunch of Time Integrators for Quantum/Classical Molecular Dynamics. In: P. Deuflhard, J. Hermans, B. Leimkuhler, A.E. Mark, S. Reich, R.D. Skeel (eds.), Computational Molecular Dynamics: Challenges, Methods, Ideas, volume 4 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, Berlin, 1997, pp. 421-432
9. Hochbruck, M., Lubich, Ch.: On Krylov subspace approximations to the matrix exponential operator. SIAM J. Numer. Anal. 34, 1911-1925 (1997)
10. Hochbruck, M., Lubich, Ch.: A Gautschi-type method for oscillatory second-order differential equations. Numer. Math. 83, 403-426 (1999)
11. Hochbruck, M., Lubich, Ch., Selhofer, H.: Exponential integrators for large systems of differential equations. SIAM J. Sci. Comp. 19, 1552-1574 (1998)
12. Iserles, A.: Think globally, act locally: solving highly-oscillatory ordinary differential equations. Appld. Num. Anal. 43, 145-160 (2002)
13. Izaguirre, J.A., Reich, S., Skeel, R.D.: Longer time steps for molecular dynamics. J. Chemical Phys. 110(20), 9853-9864 (1999)
14. Petzold, L., Jay, L., Yen, J.: Numerical Solution of Highly Oscillatory Ordinary Differential Equations. Acta Numerica 6, 437-484 (1997)