@article{MAKHILLJEAS2019141918499,
    title = {An Optimized Runge-Kutta Method for the Numerical Solution of the
Oscillatory Problems},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {14},
    number = {19},
    pages = {7077-7083},
    year = {2019},
    issn = {1816-949x},
    doi = {jeasci.2019.7077.7083},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2019.7077.7083},
    author = {Firas,A.M.,P.E. and},
    keywords = {Amplification error,numerical analysis,ordinary differential equation,oscillatory problems,phase
lag,Runge-Kutta method},
    abstract = {In this study, an optimized explicit Runge-Kutta (RK) method which is based on a method of Dormand
with six-stage and fifth algebraic order with FSAL property denoted as the ORK5 method is constructed. The
proposed method solves first-order Ordinary Differential Equations (ODEs) by first converting the second order
ODEs to an equivalent first order. The new method has zero phase-lag, zero amplification error and zero first
derivative of the phase-lag. Absolute stability of the new method is as well shown. The numerical experiments
are carried out to show the efficiency of the derived method in comparison with other existing RK methods.}
    }