Abstract
The second-order ordinary differential equation (ODE) often emerges from applied science, such as orbital mechanics, quantum mechanics, physical chemistry, electronics. As we all know, Runge-Kutta-Nyström (RKN) method is indispensable when solving the second-order ODE. In addition, there are also some intrinsic properties in these fields. How to preserve these properties must be considered when seeking the numerical solutions. Thus, in this paper, we focus on the construction of the implicit RKN method. Combining the symmetry conditions and symplecticness conditions, sixth-order implicit exponentially fitted/trigonometrically fitted RKN integrators are obtained. The designed methods have the power of solving Hamiltonian system. And we make some numerical experiments to show the efficiency and competence of the new methods compared with some highly efficient implicit codes in the literature.
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This work was supported by the Key Program of Cangzhou Jiaotong College (HB202001002) and (HBJY19023).
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This work was supported by the Key Program of Cangzhou Jiaotong College (HB202001002).
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Zhai, W., Fu, S., Zhou, T. et al. Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving \(y''=f(t,y)\). J. Appl. Math. Comput. 68, 1449–1466 (2022). https://doi.org/10.1007/s12190-021-01575-0
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DOI: https://doi.org/10.1007/s12190-021-01575-0