Fully parallel Runge-Kutta-Nyström methods for ODEs with oscillating solutions (Q686550)

This paper deals with Runge-Kutta-Nyström methods, whose coefficient matrix \(A\) is diagonal. Indeed the algebraic order of these methods is at most two or three but the dispersive order is increasing with the stage number and the methods still remain \(P\)-stable. Two- and three-stage methods are constructed which are very useful in integrating oscillatory problems. Numerical tests are given.