Low Stage and High Order Explicit Runge--Kutta Methods via $Q$- and $D$-Conditions: Several Construction Details

Junyuan He; Jizu Huang

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arXiv · 2605.16995

Low Stage and High Order Explicit Runge--Kutta Methods via $Q$- and $D$-Conditions: Several Construction Details

Junyuan He·Jizu Huang

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Abstract

This note provides additional details on the construction of the $Q$/$D$-space framework for sufficient order conditions of explicit Runge--Kutta (ERK) methods. Specifically, it presents a general version of the sufficiency theorem, several examples illustrating the verification of the sufficient conditions, a detailed construction of an ERK scheme of order $p=10$, the assembly of the associated linear systems, a complexity analysis of the construction algorithm, and tables of coefficients for the constructed ERK methods.

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Junyuan He, Jizu Huang. 2026-05-16. Low Stage and High Order Explicit Runge--Kutta Methods via $Q$- and $D$-Conditions: Several Construction Details. https://arxiv.org/abs/2605.16995

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