A Phase-Fitted Runge-Kutta-Nyström method for the Numerical Solution of Initial Value Problems with Oscillating Solutions
For researchers solving oscillatory problems in physics and engineering, this method offers improved efficiency over existing approaches, though it is an incremental improvement on an established numerical technique.
The paper develops a new Runge-Kutta-Nyström method with infinite phase-lag order for solving second-order periodic initial-value problems, demonstrating through numerical tests that it is significantly more efficient than the classical fourth-order Dormand-Prince method.
A new Runge-Kutta-Nyström method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince Runge-Kutta-Nyström method of algebraic order four\cite{pa}. Numerical illustrations indicate that the new method is much more efficient than the classical one.