A Phase-Fitted Runge-Kutta-Nystr\"om method for the Numerical Solution of Initial Value Problems with Oscillating Solutions

TL;DR

This paper introduces a new phase-fitted Runge-Kutta-Nyström method with infinite phase-lag order, designed to efficiently solve second-order periodic initial-value problems with oscillating solutions.

Contribution

A novel phase-fitted Runge-Kutta-Nyström method with infinite phase-lag order, improving efficiency for oscillatory second-order problems.

Findings

The new method outperforms classical methods in efficiency.

Numerical tests confirm higher accuracy for oscillatory problems.

The method is particularly effective for periodic initial-value problems.

Abstract

A new Runge-Kutta-Nystr\"om 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-Nystr\"om method of algebraic order four\cite{pa}. Numerical illustrations indicate that the new method is much more efficient than the classical one.