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Abstract
The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods of Gauss type for the numerical integration of Hamiltonian systems with oscillatory solutions is revisited. In this paper new such two-, three- and four-step integrators are constructed and discussed 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 for three-stage methods.
Keywords
Exponential fitting, oscillatory Hamiltonian, RK-methods, symplecticness

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Chicago
Vanden Berghe, Guido, and Marnix Van Daele. 2010. “Symplectic Exponentially-fitted Modified Runge-Kutta Gauss Methods.” In Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010, ed. Jesus Vigo-Aguiar, 945–960. Almería, Spain: Universidad de Almería.
APA
Vanden Berghe, Guido, & Van Daele, M. (2010). Symplectic exponentially-fitted modified Runge-Kutta Gauss methods. In J. Vigo-Aguiar (Ed.), Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010 (pp. 945–960). Presented at the 10th International conference on Computational and Mathematical Methods in Science and Engineering (CMMSE 2010), European section, Almería, Spain: Universidad de Almería.
Vancouver
1.
Vanden Berghe G, Van Daele M. Symplectic exponentially-fitted modified Runge-Kutta Gauss methods. In: Vigo-Aguiar J, editor. Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010. Almería, Spain: Universidad de Almería; 2010. p. 945–60.
MLA
Vanden Berghe, Guido, and Marnix Van Daele. “Symplectic Exponentially-fitted Modified Runge-Kutta Gauss Methods.” Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010. Ed. Jesus Vigo-Aguiar. Almería, Spain: Universidad de Almería, 2010. 945–960. Print.
@inproceedings{1001679,
  abstract     = {The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods of Gauss type for the numerical integration of Hamiltonian systems with oscillatory solutions is revisited. In this paper new such two-, three- and four-step integrators are constructed and discussed 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 for three-stage methods.},
  author       = {Vanden Berghe, Guido and Van Daele, Marnix},
  booktitle    = {Proceedings of the 10th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2010},
  editor       = {Vigo-Aguiar, Jesus},
  isbn         = {9788461355105},
  keyword      = {Exponential fitting,oscillatory Hamiltonian,RK-methods,symplecticness},
  language     = {eng},
  location     = {Almer{\'i}a, Spain},
  pages        = {945--960},
  publisher    = {Universidad de Almer{\'i}a},
  title        = {Symplectic exponentially-fitted modified Runge-Kutta Gauss methods},
  year         = {2010},
}