Abstract
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 dy dx = iwy , 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.
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