A new embedded phase-fitted modified Runge-Kutta method for the numerical solution of oscillatory problems - Fawzi, F. A.; Senu, N.; Ismail, F.; Majid, Z. A. (Hikari, 2016)
In this work, a new way for constructing an efficiently modified Runge-Kutta (RK) method to solve first-order ordinary differential equations with oscillatory solutions is provided. The proposed method solves the first-order ODEs by first converting the second order ODEs to an equivalent first-order ODEs. The method of the embedded has algebraic orders five and four. The numerical results of the new method have been compared with those of existing methods and showed that the new method is more efficient.