Symmetric and symplectic exponentially fitted Runge–Kutta–Nyström methods for Hamiltonian problems

Xiong You and Bingzhen Chen

Mathematics and Computers in Simulation (MATCOM), 2013, vol. 94, issue C, 76-95

Abstract: The construction of symmetric and symplectic exponentially fitted modified Runge–Kutta–Nyström (SSEFRKN) methods is considered. Based on the symmetry, symplecticity, and exponentially fitted conditions, new explicit modified RKN integrators with FSAL property are obtained. The new integrators integrate exactly differential systems whose solutions can be expressed as linear combinations of functions from the set {exp(±iωt)}, ω>0, i2=−1, or equivalently from the set {cos(ωt), sin(ωt)}. The phase properties of the new integrators are examined and their periodicity regions are obtained. Numerical experiments are accompanied to show the high efficiency and competence of the new SSEFRKN methods compared with some highly efficient nonsymmetric symplecti EFRKN methods in the literature.

Keywords: Runge–Kutta–Nyström method; Symmetry; Symplecticity; Exponential fitting; Hamiltonian system (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:94:y:2013:i:c:p:76-95

DOI: 10.1016/j.matcom.2013.05.010

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