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Journal of Applied Mathematics and Computing

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14-06-2021 | Original Research

Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving \(y''=f(t,y)\)

Authors: Wenjuan Zhai, Shuhuan Fu, Tianchong Zhou, Chun Xiu

Published in: Journal of Applied Mathematics and Computing | Issue 2/2022

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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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Title: Exponentially-fitted and trigonometrically-fitted implicit RKN methods for solving
Authors: Wenjuan Zhai
Shuhuan Fu
Tianchong Zhou
Chun Xiu
Publication date: 14-06-2021
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 2/2022
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01575-0

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