Explicit Runge-Kutta methods for initial value problems with oscillating solutions (Q5961655)

New pairs of embedded Runge-Kutta (RK) methods for the numerical solution of systems of first-order differential equations with oscillating solutions are obtained.NEWLINENEWLINENEWLINEA family of RK pairs with nine stages and algebraic orders seven and five depending on five parameters is constructed. Three optimal pairs are selected within this family taking into account the criteria of accuracy, stability, reliability of stepsize estimator and the orders of dispersion and/or dissipation which play an important role in the numerical integration of problems with oscillating solutions.NEWLINENEWLINENEWLINEFinally, the pair denoted by RK[7(5),10,9], which is dispersive of order 10 and dissipative of order 9, is found to be the most efficient one among the three selected pairs by testing their behavior with an extensive set of numerical experiments.