Abstract
An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted pair can exactly integrate (except round-off errors) the common test: y″=−w2y. The local truncation error of the new method is derived, and we show that the order of convergence is maintained. The stability analysis is addressed, and we demonstrate that the developed method is absolutely stable, and thus appropriate for solving stiff problems. The numerical experiments show a better performance of the new embedded pair in comparison with other existing RKN pairs of similar characteristics.
Funder
King Mongkut's University of Technology Thonburi
Subject
Applied Mathematics,Computational Mathematics,General Engineering
Reference25 articles.
1. Classical Eight and Lower-Order Runge–Kutta–Nyström Formulas with Step-Size Control for Special Second-Order Differential Equations;Fehlberg,1972
2. A 5(3) pair of explicit Runge–Kutta–Nyström methods for oscillatory problems
3. A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators
4. An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions
5. Construction of trigonometrically and exponentially fitted Runge–Kutta–Nyström methods for the numerical solution of the Schrödinger equation and related problems—A method of 8th algebraic order;Kalogiratou;J. Math.,2002
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