Functionally fitted Runge-Kutta-Nystr\"{o}m methods
Numerical Analysis
2014-10-17 v1
Abstract
We have shown previously that functionally fitted Runge-Kutta (FRK) methods can be studied using a convenient collocation framework. Here, we extend that framework to functionally fitted Runge-Kutta-Nystr\"om (FRKN) methods, shedding further light on the fact that these methods can integrate a second-order differential equation exactly if its solution is a combination of certain basis functions, and that superconvergence can be obtained when the collocation points satisfy some orthogonality conditions. An analysis of their stability is also conducted.
Cite
@article{arxiv.1410.4287,
title = {Functionally fitted Runge-Kutta-Nystr\"{o}m methods},
author = {N. S. Hoang and R. B. Sidje},
journal= {arXiv preprint arXiv:1410.4287},
year = {2014}
}
Comments
19 pages, 2 figures