A Runge-Kutta Fehlberg method with phase-lag of order infinity for initial-value problems with oscillating solution

Abstract A Runge-Kutta method is developed for the numerical solution of initial-value problems with oscillating solution. Based on the Runge-Kutta Fehlberg 2(3) method, a Runge-Kutta method with phase-lag of order infinity is developed. Based on these methods we produce a new embedded Runge-Kutta Fehlberg 2(3) method with phase-lag of order infinity. This method is called as Runge-Kutta Fehlberg Phase Fitted method (RKFPF). The numerical results indicate that this new method is much more efficient, compared with other well-known Runge-Kutta methods, for the numerical solution of differential equations with oscillating solution, using variable step size.

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