Nystrom Methods in the RKQ Algorithm for Initial-value Problems
Numerical Analysis
2023-11-28 v3 Numerical Analysis
Abstract
We incorporate explicit Nystrom methods into the RKQ algorithm for stepwise global error control in numerical solutions of initial-value problems. The initial-value problem is transformed into an explicitly second-order problem, so as to be suitable for Nystrom integration. The Nystrom methods used are fourth-order, fifth-order and 10th-order. Two examples demonstrate the effectiveness of the algorithm.
Keywords
Cite
@article{arxiv.1110.6749,
title = {Nystrom Methods in the RKQ Algorithm for Initial-value Problems},
author = {J. S. C. Prentice},
journal= {arXiv preprint arXiv:1110.6749},
year = {2023}
}
Comments
This is an extension of ideas published in J. Math. Res. (open access); see refs [1] and [2]