Advanced search
1 file | 364.25 KB

Symplectic exponentially-fitted four stage Runge-Kutta methods of the Gauss type

(2011) NUMERICAL ALGORITHMS. 56(4). p.591-608
Author
Organization
Abstract
The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions deserves a lot of interest. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators of eighth-order are studied and constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (2004). Numerical experiments for some oscillatory problems are presented.
Keywords
Symplecticness, Exponential fitting, RK-methods, Oscillatory Hamiltonian systems, NUMERICAL-INTEGRATION

Downloads

  • (...).pdf
    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 364.25 KB

Citation

Please use this url to cite or link to this publication:

Chicago
Vanden Berghe, Guido, and Marnix Van Daele. 2011. “Symplectic Exponentially-fitted Four Stage Runge-Kutta Methods of the Gauss Type.” Numerical Algorithms 56 (4): 591–608.
APA
Vanden Berghe, Guido, & Van Daele, M. (2011). Symplectic exponentially-fitted four stage Runge-Kutta methods of the Gauss type. NUMERICAL ALGORITHMS, 56(4), 591–608.
Vancouver
1.
Vanden Berghe G, Van Daele M. Symplectic exponentially-fitted four stage Runge-Kutta methods of the Gauss type. NUMERICAL ALGORITHMS. 2011;56(4):591–608.
MLA
Vanden Berghe, Guido, and Marnix Van Daele. “Symplectic Exponentially-fitted Four Stage Runge-Kutta Methods of the Gauss Type.” NUMERICAL ALGORITHMS 56.4 (2011): 591–608. Print.
@article{1182870,
  abstract     = {The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions deserves a lot of interest. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators of eighth-order are studied and constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (2004). Numerical experiments for some oscillatory problems are presented.},
  author       = {Vanden Berghe, Guido and Van Daele, Marnix},
  issn         = {1017-1398},
  journal      = {NUMERICAL ALGORITHMS},
  keyword      = {Symplecticness,Exponential fitting,RK-methods,Oscillatory Hamiltonian systems,NUMERICAL-INTEGRATION},
  language     = {eng},
  number       = {4},
  pages        = {591--608},
  title        = {Symplectic exponentially-fitted four stage Runge-Kutta methods of the Gauss type},
  url          = {http://dx.doi.org/10.1007/s11075-010-9407-8},
  volume       = {56},
  year         = {2011},
}

Altmetric
View in Altmetric
Web of Science
Times cited: