A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems

  1. Demba, Musa Ahmed
  2. Ramos, Higinio
  3. Kumam, Poom
  4. Watthayu, Wiboonsak
Journal:
Mathematical and Computational Applications

ISSN: 2297-8747

Year of publication: 2021

Volume: 26

Issue: 3

Pages: 59

Type: Article

DOI: 10.3390/MCA26030059 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Mathematical and Computational Applications

Abstract

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with fourstages using phase-fitted and amplification-fitted techniques is developed in this paper. The newadapted pair can exactly integrate (except round-off errors) the common test: y00 = −w2y. Thelocal truncation error of the new method is derived, and we show that the order of convergence ismaintained. The stability analysis is addressed, and we demonstrate that the developed method isabsolutely stable, and thus appropriate for solving stiff problems. The numerical experiments showa better performance of the new embedded pair in comparison with other existing RKN pairs ofsimilar characteristics

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Bibliographic References

  • Fehlberg, (1972)
  • 10.1016/j.mcm.2006.07.016
  • 10.1016/j.cam.2003.03.002
  • 10.1016/S0010-4655(98)00088-5
  • Kalogiratou, (2002), J. Math., 31, pp. 211
  • 10.1016/j.newast.2006.03.001
  • 10.1007/s10910-012-0127-2
  • 10.1088/0031-8949/80/01/015005
  • 10.1016/j.amc.2014.11.097
  • 10.1016/j.cam.2014.07.016
  • 10.1016/j.apnum.2006.02.003
  • 10.1007/s10114-018-6300-1
  • 10.1016/j.jcp.2016.07.033
  • 10.1016/j.cpc.2009.05.010
  • 10.12988/ams.2017.7262
  • 10.3390/mca21040046
  • 10.3390/computation8020032
  • Hairer, (2008)
  • 10.1137/0726023
  • 10.1016/j.cpc.2004.12.011
  • Tsitouras, (2012), Comput. Phys. Commun., 183, pp. 470, 10.1016/j.cpc.2011.11.002
  • 10.1016/S0010-4655(99)00365-3
  • 10.1016/j.apm.2009.12.004
  • 10.1016/j.aml.2010.07.003
  • 10.1016/j.cam.2014.09.008