Ghent University Academic Bibliography

Advanced

Symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type, revisited

Guido Vanden Berghe UGent and Marnix Van Daele UGent (2011) Recent advances in computational and applied mathematics. p.591-608
abstract
The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentiallyfitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators are constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (Exponential fitting, Kluwer Academic Publishers, 2004). Numerical experiments for some oscillatory problems are presented and compared to the results obtained by previous methods.
Please use this url to cite or link to this publication:
author
organization
year
type
bookChapter
publication status
published
subject
keyword
symplecticness, Oscillatory, RK-methods, Exponential fitting, Hamiltonian Systems
book title
Recent advances in computational and applied mathematics
editor
Theodore Simos
pages
591 - 608
publisher
Springer
place of publication
Dordrecht, Netherlands; New-York, US
ISBN
9789048199808
language
English
UGent publication?
yes
classification
B2
copyright statement
I have transferred the copyright for this publication to the publisher
VABB id
c:vabb:339855
VABB type
VABB-4
id
1182851
handle
http://hdl.handle.net/1854/LU-1182851
date created
2011-03-08 10:29:32
date last changed
2017-01-02 09:53:53
@incollection{1182851,
  abstract     = {The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentiallyfitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators are constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (Exponential fitting, Kluwer Academic Publishers, 2004). Numerical experiments for some oscillatory problems are presented and compared to the results obtained by previous methods.},
  author       = {Vanden Berghe, Guido and Van Daele, Marnix},
  booktitle    = {Recent advances in computational and applied mathematics},
  editor       = {Simos, Theodore},
  isbn         = {9789048199808},
  keyword      = {symplecticness,Oscillatory,RK-methods,Exponential fitting,Hamiltonian Systems},
  language     = {eng},
  pages        = {591--608},
  publisher    = {Springer},
  title        = {Symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type, revisited},
  year         = {2011},
}

Chicago
Vanden Berghe, Guido, and Marnix Van Daele. 2011. “Symplectic Exponentially-fitted Modified Runge-Kutta Methods of the Gauss Type, Revisited.” In Recent Advances in Computational and Applied Mathematics, ed. Theodore Simos, 591–608. Dordrecht, Netherlands; New-York, US: Springer.
APA
Vanden Berghe, Guido, & Van Daele, M. (2011). Symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type, revisited. In Theodore Simos (Ed.), Recent advances in computational and applied mathematics (pp. 591–608). Dordrecht, Netherlands; New-York, US: Springer.
Vancouver
1.
Vanden Berghe G, Van Daele M. Symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type, revisited. In: Simos T, editor. Recent advances in computational and applied mathematics. Dordrecht, Netherlands; New-York, US: Springer; 2011. p. 591–608.
MLA
Vanden Berghe, Guido, and Marnix Van Daele. “Symplectic Exponentially-fitted Modified Runge-Kutta Methods of the Gauss Type, Revisited.” Recent Advances in Computational and Applied Mathematics. Ed. Theodore Simos. Dordrecht, Netherlands; New-York, US: Springer, 2011. 591–608. Print.