A novel energy-preserving relaxation extended Runge–Kutta Nyström framework for oscillatory Hamiltonian systems

Ting Fu, Xu Qian, SongHe Song and Hong Zhang

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 240, issue C, 1023-1040

Abstract: We propose a novel energy-preserving schemes for general oscillatory Hamiltonian systems that preserve the original energy and demonstrate better long-time numerical behavior. These schemes are constructed by using the relaxation idea and the extended Runge–Kutta Nyström (ERKN) methods. The stability regions and the accuracy of these novel schemes are analyzed. We prove the existence of the relaxation parameters and present their estimation. Several numerical examples are provided to illustrate all the above results.

Keywords: Relaxation technique; Extended Runge–Kutta Nyström (ERKN) methods; Stability; Oscillatory system; Energy-preserving numerical methods (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:240:y:2026:i:c:p:1023-1040

DOI: 10.1016/j.matcom.2025.08.011

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