Abstract
The purpose of the present work is to construct a new Runge–Kutta pair of orders five and four to outperform the state-of-the-art in these kind of methods when addressing problems with periodic solutions. We consider the family of such pairs that the celebrated Dormand–Prince pair also belongs. The chosen family comes with coefficients that all depend on five free parameters. These latter parameters are tuned in a way to furnish a new method that performs best on a couple of oscillators. Then, we observe that this trained pair outperforms other well known methods in the relevant literature in a standard set of problems with periodic solutions. This is remarkable since no special property holds such as high phase-lag order or an extended interval of periodicity.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference25 articles.
1. On Runge-Kutta processes of high order
2. Numerical Methods for Ordinary Differential Equations;Butcher,2003
3. The Art of Writing a runge-kutta Cosde. II;Shampine;Appl. Math. Comput.,1979
4. Ueber die numerische Aufl�sung von Differentialgleichungen
5. Beitrag zur naherungsweisen Integration von Differentialgleichungen;Kutta;Z. Math. Phys.,1901
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