A high-order explicit Runge-Kutta pair for initial value problems with oscillating solutions

A new Runge-Kutta-pair of orders eight and seven is presented here. The proposed pair when applied with small step-size to the test equation , w real, has amplification factors very near to unit. This is very important then, because the numerical solution stays close to the cyclic solution of the test problem. Numerical tests over a set of problems with oscillating solutions demonstrate the superiority of the new pair.