Symplectic exponentially-fitted four-stage Runge-Kutta methods of the Gauss type. (English) Zbl 1215.65130
Summary: 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 L. Gr. Ixaru and G. Vanden Berghe [Exponential Fitting. Mathematics and its Applications (Dordrecht) 568. Dordrecht: Kluwer Academic Publishers (2004; Zbl 1105.65082)]. Numerical experiments for some oscillatory problems are presented.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Citations:
Zbl 1105.65082References:
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