Abstract
An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y″=−w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics.
Highlights
A Phase-Fitted and Amplification-Fitted ExplicitMusa Ahmed Demba 1,2,3,† , Higinio Ramos 4,5,† , Poom Kumam 3,4,6,† , Wiboonsak Watthayu 6, *,†
Fang et al developed a new pair of explicit ARKN methods in [11], for the numerical integration of general perturbed oscillators
The new adapted RKN pair will be named as PFAFRKN5(3)
Summary
Musa Ahmed Demba 1,2,3,† , Higinio Ramos 4,5,† , Poom Kumam 3,4,6,† , Wiboonsak Watthayu 6, *,†.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
