Runge-Kutta-Nystrom methods with equation dependent coefficients and reduced phase lag for oscillatory problems

被引：0
|
作者：
Yang, Yanping [1 ]
You, Xiong [2 ]
Fang, Yonglei [1 ]
机构：
[1] Zaozhuang Univ, Sch Math & Stat, Zaozhuang 277160, Peoples R China
[2] Nanjing Agr Univ, Coll Sci, Nanjing 210095, Jiangsu, Peoples R China
来源：
JOURNAL OF MATHEMATICAL CHEMISTRY | 2017年 / 55卷 / 01期
关键词：
Oscillatory problems; Equation dependent coefficient; Dispersion; Dissipation; INITIAL-VALUE-PROBLEMS; TRIGONOMETRICALLY-FITTED METHODS; SCHRODINGER-EQUATION; NUMERICAL-SOLUTION; EXPLICIT; FREQUENCY; INTEGRATION; ALGORITHMS; CHOICE; ERRORS;
D O I：
10.1007/s10910-016-0685-9
中图分类号：
O6 [化学];
学科分类号：
0703 ;
摘要：
A new family of one-parameter equation dependent Runge-Kutta-Nystrom (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.
引用
收藏
页码：259 / 277
页数：19
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