Runge–Kutta–Nyström methods with equation dependent coefficients and reduced phase lag for oscillatory problems

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• 作者：Yanping Yang ; Xiong You ; Yonglei Fang
• 关键词：Oscillatory problems ; Equation dependent coefficient ; Dispersion ; Dissipation
• 刊名：Journal of Mathematical Chemistry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：55
• 期：1
• 页码：259-277
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Physical Chemistry; Theoretical and Computational Chemistry; Math. Applications in Chemistry;
• 出版者：Springer International Publishing
• ISSN：1572-8897
• 卷排序：55

文摘

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.