Nystrom Methods in the RKQ Algorithm for Initial-value Problems
J. S. C. Prentice
TL;DR
This paper integrates Nystrom methods of various orders into the RKQ algorithm to improve global error control in solving initial-value problems, demonstrating effectiveness through examples.
Contribution
It introduces a novel approach combining Nystrom methods with RKQ for enhanced error control in initial-value problem solutions.
Findings
Effective stepwise error control demonstrated
Higher-order Nystrom methods improve accuracy
Algorithm validated with two examples
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNumerical methods for differential equations · Computational Fluid Dynamics and Aerodynamics · Model Reduction and Neural Networks