Skip to main content
Log in

Error Bounds for Exponential Operator Splittings

  • Published:
BIT Numerical Mathematics Aims and scope Submit manuscript

Abstract

Error bounds for the Strang splitting in the presence of unbounded operators are derived in a general setting and are applied to evolutionary Schrödinger equations and their pseudo-spectral space discretization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. O. Dia and M. Schatzman, An estimate of the Kac transfer operator, J. Funct. Anal., 145 (1997), pp. 108-135.

    Google Scholar 

  2. A. Doumeki, T. Ichinose, and H. Tamura, Error bounds on exponential product formulas for Schrödinger operators, J. Math. Soc. Japan, 50 (1998), pp. 359-377.

    Google Scholar 

  3. B. Helffer, Around the transfer operator and the Trotter-Kato formula, in Partial Differential Operators and Mathematical Physics, M. Demuth et al., eds., Oper. Theor. Adv. Appl., Vol. 78, Birkhäuser, Basel, 1995, pp. 161-174.

    Google Scholar 

  4. T. Jahnke, Splittingverfahren für Schrödingergleichungen, Wiss. Arbeit für das Staatsexamen, Math. Institut, Univ. Tübingen, 1999.

    Google Scholar 

  5. R. Kozlov and B. Owren, Order reduction in operator splitting methods, Preprint Numerics 6/1999, University of Trondheim, 1999.

  6. S. T. Kuroda and K. Kurata, Product formulas and error estimates, in Partial Differential Operators and Mathematical Physics, M. Demuth et al., eds., Oper. Theor. Adv. Appl., Vol. 78, Birkhäuser, Basel, 1995, pp. 213-220.

    Google Scholar 

  7. H. Neidhardt and V. A. Zagrebnov, On error estimates for the Trotter-Kato product formula, Letters Math. Phys., 44 (1998), pp. 169-186.

    Google Scholar 

  8. Dzh. L. Rogava, Error bounds for Trotter-type formulas for self-adjoint operators, Funct. Anal. Appl., 27 (1993), pp. 217-219.

    Google Scholar 

  9. Q. Sheng, Global error estimates for exponential splitting, IMA J. Numer. Anal., 14 (1994), pp. 27-56.

    Google Scholar 

  10. B. Sportisse and J. G. Verwer, A note on operator splitting in the stiff linear case, Tech. Report MAS-R 9830, CWI Amsterdam, 1998.

    Google Scholar 

  11. G. Strang, On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5 (1968), pp. 506-517.

    Google Scholar 

  12. H. F. Trotter, On the product of semi-groups of operators, Proc. Amer. Math. Soc., 10 (1959), pp. 545-551.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jahnke, T., Lubich, C. Error Bounds for Exponential Operator Splittings. BIT Numerical Mathematics 40, 735–744 (2000). https://doi.org/10.1023/A:1022396519656

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022396519656

Navigation