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arXiv · 2604.19068

Taylor Tube Method for Validated IVP

Bingwei Zhang·Chee Yap
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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.

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Bingwei Zhang, Chee Yap. 2026-04-21. Taylor Tube Method for Validated IVP. https://arxiv.org/abs/2604.19068

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