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

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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.
Keywords
symplecticness, Oscillatory, RK-methods, Exponential fitting, Hamiltonian Systems

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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.
@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},
}