65 citations · 66 across the 4 of their papers we have counts for
5 papers
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…
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…
Isomeric trees and the order of Runge--Kutta methods
John C. Butcher, Helmut Podhaisky
The conditions for a Runge--Kutta method to be of order with for a scalar non-autonomous problem are a proper subset of the order conditions for a vector problem. Neve…
Symmetric general linear methods
John Butcher, Adrian Hill, Terrence Norton
The article considers symmetric general linear methods, a class of numerical time integration methods which, like symmetric Runge--Kutta methods, are applicable to general time--re…
A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems
Yuto Miyatake, John C. Butcher
High order energy-preserving methods for Hamiltonian systems are presented. For this aim, an energy-preserving condition of continuous stage Runge--Kutta methods is proved. Order c…