TY  - JOUR
T1  - An Optimized Runge-Kutta Method for the Numerical Solution of the
Oscillatory Problems
AU - A. Fawzi, Firas AU - Gaftan, A.M. AU - Oguntunde, P.E. AU - Senu, N. 
JO  - Journal of Engineering and Applied Sciences
VL  - 14
IS  - 19
SP  - 7077
EP  - 7083
PY  - 2019
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2019.7077.7083
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2019.7077.7083
KW  - Amplification error
KW  -numerical analysis
KW  -ordinary differential equation
KW  -oscillatory problems
KW  -phase
lag
KW  -Runge-Kutta method
AB  - 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.
ER  -