A zero-dissipative phase-fitted fourth order diagonally implicit Runge-Kutta-Nyström method for solving oscillatory problems (Q1719536)

Summary: A new diagonally implicit Runge-Kutta-Nyström (DIRKN) method is constructed for solving second order differential equations with oscillatory solutions. The method is originally based on existing DIRKN method derived by Senu et al. which is three-stage and fourth algebraic order. The new derived method has a variable coefficient with phase-lag of order infinity. The numerical experiments are carried out and the results show the efficiency and accuracy of the new method in comparison with the other DIRKN methods in the literature.