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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.19068 |
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| _version_ | 1866917425082007552 |
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| author | Zhang, Bingwei Yap, Chee |
| author_facet | Zhang, Bingwei Yap, Chee |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Taylor Tube Method for Validated IVP Zhang, Bingwei Yap, Chee Numerical Analysis 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. |
| title | Taylor Tube Method for Validated IVP |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.19068 |