Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Butcher, John C."'
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 rely on labelled trees, whereas recent developments in B-series analys
Externí odkaz:
http://arxiv.org/abs/2409.08533
In this paper, we propose linearly implicit and arbitrary high-order conservative numerical schemes for ordinary differential equations with a quadratic invariant. Many differential equations have invariants, and numerical schemes for preserving them
Externí odkaz:
http://arxiv.org/abs/2203.00944
Autor:
Butcher, John C., Podhaisky, Helmut
The conditions for a Runge--Kutta method to be of order $p$ with $p\ge 5$ for a scalar non-autonomous problem are a proper subset of the order conditions for a vector problem. Nevertheless, Runge--Kutta methods that were derived historically only for
Externí odkaz:
http://arxiv.org/abs/2112.01608
Publikováno v:
In Applied Numerical Mathematics May 2023 187:71-88
Autor:
Butcher, John C., Podhaisky, Helmut
Publikováno v:
In Journal of Computational and Applied Mathematics 1 December 2022 415
Autor:
Miyatake, Yuto, Butcher, John C.
Publikováno v:
SIAM J. Numer. Anal. 54(3) 1993-2013
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 conditions are simplified and parallelizable conditions are also given.
Externí odkaz:
http://arxiv.org/abs/1505.02537
Autor:
Butcher, John C.1 (AUTHOR) butcher@math.auckland.ac.nz
Publikováno v:
Axioms (2075-1680). May2022, Vol. 11 Issue 5, p184. 6p.
Autor:
MIYATAKE, YUTO, BUTCHER, JOHN C.
Publikováno v:
SIAM Journal on Numerical Analysis, 2016 Jan 01. 54(3), 1993-2013.
Externí odkaz:
http://www.jstor.org/stable/43901749
Publikováno v:
SIAM Journal on Numerical Analysis, 2014 Jan 01. 52(5), 2440-2465.
Externí odkaz:
http://www.jstor.org/stable/24512201