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Título
A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems.
Autor(es)
Materia
Phase-fitted and amplification-fitted schemes
RKN pair
Oscillatory systems
Initial-value problems
Clasificación UNESCO
12 Matemáticas
Fecha de publicación
2021
Editor
MDPI
Citación
Demba, M.A.; Ramos, H.; Kumam, P.; Watthayu, W. A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems. Math. Comput. Appl. 2021, 26, 59. https://doi.org/10.3390/mca26030059
Resumen
[EN]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.
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