Abstract
A new family of one-parameter equation dependent Runge–Kutta–Nyström (EDRKN) methods for the numerical solution of second–order differential equations are investigated. The coefficients of new three-stage EDRKN methods are obtained by nullifying up to appropriate order of moments of operators related to the internal and external stages. A fifth-order EDRKN method that is dispersive of order six and dissipative of order five and a fourth-order EDRKN method that is dispersive of order four and zero-dissipative are derived. Phase analysis shows that there exist no explicit EDRKN methods that are P-stable. Numerical experiments are reported to show the high accuracy and efficiency of the new EDRKN methods.
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Acknowledgments
The authors are deeply grateful to the anonymous referees, for their valuable comments and suggestions. This research was partially supported by NSFC (Nos. 11571302, 11171155), the foundation of Scientific Research Project of Shandong Universities (No. J14LI04) and the Fundamental Research Fund for the Central Universities (No. KYZ201424).
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Yang, Y., You, X. & Fang, Y. Runge–Kutta–Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems. J Math Chem 55, 259–277 (2017). https://doi.org/10.1007/s10910-016-0685-9
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DOI: https://doi.org/10.1007/s10910-016-0685-9