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Phase-type representations for Strong Stability Preserving Runge--Kutta methods

  • Haijun Yu
  • Quanfan Zhu
  • Zhanyang Weng
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Abstract

We develop a phase-type (PH) representation of strong stability preserving (SSP) Runge--Kutta (RK) methods. This representation provides a probabilistic interpretation of the RK coefficients and translates the chain order conditions into absorption-time moment identities. Using moment ratio bounds for PH distributions, we prove the conjectured optimal SSP coefficients for general implicit RK methods of orders two and three. The equality characterizations also establish uniqueness of the optimal RK tableaux.

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Cite

BibTeXRIS
BibTeX
@misc{yu2026phasetype,
  title = {{Phase-type representations for Strong Stability Preserving Runge--Kutta methods}},
  author = {Haijun Yu and Quanfan Zhu and Zhanyang Weng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37425},
  eprint = {2610.37425},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37425},
}
RIS
TY  - UNPB
TI  - Phase-type representations for Strong Stability Preserving Runge--Kutta methods
AU  - Haijun Yu
AU  - Quanfan Zhu
AU  - Zhanyang Weng
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37425
UR  - https://arxiv.org/abs/2610.37425
AB  - We develop a phase-type (PH) representation of strong stability preserving (SSP) Runge--Kutta (RK) methods. This representation provides a probabilistic interpretation of the RK coefficients and translates the chain order conditions into absorption-time moment identities. Using moment ratio bounds for PH distributions, we prove the conjectured optimal SSP coefficients for general implicit RK methods of orders two and three. The equality characterizations also establish uniqueness of the optimal RK tableaux.
ER  -