Year: 2026
Type: preprint
Abstract: We recently introduced a novel architecture for the design of validated IVP algorithms. This architecture forms the basis of our complete validated algorithm for IVP. A key subroutine in our algorithm is the \textbf{Euler Tube}: it gave a technique for refining end- and full-enclosures and is also key to deriving a complexity bound of our IVP solver. In this paper, we generalize it to \textbf{Taylor Tube} of degree $p\ge 1$. As expected, higher-degree Taylor Tubes improve accuracy. But surprisingly, our experiments show that it can also lead to an overall speedup when combined with bisection.
Source: arXiv (Cornell University)
Authors: Zhang, Bingwei, Yap, Chee
Institution: Courant Institute of Mathematical Sciences
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7155225540
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