An embedded pair of exponentially fitted explicit Runge–Kutta methods

An embedded pair of exponentially fitted explicit Runge–Kutta (RK) methods for the numerical integration of IVPs with oscillatory solutions is derived. This pair is based on the exponentially fitted explicit RK method constructed in Vanden Berghe et al., and we confirm that the methods which constitute the pair have algebraic order 4 and 3. Some numerical experiments show the efficiency of our pair when it is compared with the variable step code proposed by Vanden Berghe et al. (J. Comput. Appl. Math. 125 (2000) 107).