Abstract
In this study, we derive fifth-order four-stage explicit trigonometrically-fitted Runge–Kutta–Nyström (ETFRKN) methods for the numerical integration of second-order initial value problems with oscillatory solutions based on Simos technique. The numerical results show the efficiency of the proposed methods in comparison with other Runge–Kutta–Nyström (RKN) Methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bettis, D.: Zeitschrift für angewandte Mathematik und Physik ZAMP 30(4), 699 (1979)
Monovasilis, T., Kalogiratou, Z., Simos, T.: Appl. Math. Inf. Sci. 7(1), 81 (2013)
Franco, J., Gómez, I.: J. Comput. Appl. Math. 260, 482 (2014)
D’Ambrosio, R., Paternoster, B., Santomauro, G.: Appl. Math. Lett. 30, 56 (2014)
Ramos, H., Vigo-Aguiar, J.: Comput. Phys. Commun. 185(4), 1230 (2014)
Simos, T.: Comput. Phys. Commun. 115(1), 1 (1998)
Coleman, J.P., Duxbury, S.C.: J. Comput. Appl. Math. 126(1), 47 (2000)
Berghe, G.V., De Meyer, H., Van Daele, M., Van Hecke, T.: Comput. Phys. Commun. 123(1), 7 (1999)
Simos, T.E.: Appl. Math. Lett. 15(2), 217 (2002)
Senu, N.: Runge–Kutta–Nystrom methods for the solutions of oscillatory differential equations. Ph.D. Dissertation, Department of mathematics, Faculty of Science, 43400 Serdang, Malaysia (2009)
Ahmad, S., Ismail, F., Senu, N., Suleiman, M.: Appl. Math. Comput. 219(19), 10096 (2013)
Senu, N., Suleiman, M., Ismail, F., Othman, M.: WSEAS Trans. Math. 9(9), 679 (2010)
Anastassi, Z., Kosti, A.: J. Comput. Appl. Math. 275, 311 (2015)
Acknowledgments
We are thankful to the Institute of Mathematical Research (INSPEM) and the Department of Mathematics, Universiti Putra Malaysia for the support and assistance during the research work.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this paper
Cite this paper
Demba, M.A., Senu, N., Ismail, F. (2016). Fifth-Order Four-Stage Explicit Trigonometrically-Fitted Runge–Kutta–Nyström Methods. In: Kılıçman, A., Srivastava, H., Mursaleen, M., Abdul Majid, Z. (eds) Recent Advances in Mathematical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-10-0519-0_3
Download citation
DOI: https://doi.org/10.1007/978-981-10-0519-0_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-0517-6
Online ISBN: 978-981-10-0519-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)