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math.NA2024
On the B-series composition theorem
John C. Butcher, Taketomo Mitsui, Yuto Miyatake +1
The B-series composition theorem has been an important topic in numerical analysis of ordinary differential equations for the past-half century. Traditional proofs of this theorem…
math.NA2022
High-order linearly implicit schemes conserving quadratic invariants
Shun Sato, Yuto Miyatake, John C. Butcher
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differentia…