ABSTRACT
This paper concerns modified Two-Derivative Runge–Kutta–Nyström (TDRKN) methods for solving second-order initial value problems. Compromised with the deduced order and symmetry criteria, two implicit and forth-order two-stage TDRKN schemes are derived through a mixed collocation approach. Phase and periodic stability features are examined. Numerical experiments are carried out to illustrate the effectiveness and competence of our new methods. Comparisons with existing highly accurate and efficient numerical methods are given.
Acknowledgements
The authors are grateful to the referees for their valuable suggestions which helped to improve the content and presentation of the paper. Finally, the authors wish to thank Professor Qin Sheng for his invaluable help to enhance the quality and presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Julius O. Ehigie http://orcid.org/0000-0002-3159-5743
Manman Zou http://orcid.org/0000-0003-0254-8945
Xinlin Hou http://orcid.org/0000-0003-0776-2959
Xiong You http://orcid.org/0000-0002-0343-3878