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

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.