Random Sampling from the Normal Distribution. - John C. Butcher (Comput. J., 1961)

A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations. - John C. Butcher (J. ACM, 1965)

A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages. - John C. Butcher (J. ACM, 1967)

A Transformed implicit Runge-Kutta Method. - John C. Butcher (J. ACM, 1979)

Towards efficient implementation of singly-implicit methods. - John C. Butcher (ACM Trans. Math. Softw., 1988)

Theory of Difference Equations: Numerical Methods and Applications (V. Lakshmikantham and D. Trigiante). - John C. Butcher (SIAM Rev., 1989)

Order, stepsize and stiffness switching. - John Charles Butcher (Computing, 1990)

Difference Equations from Differential Equations (W. J. Lick). - John C. Butcher (SIAM Rev., 1992)

Some orbital test problems. - John C. Butcher (Computing, 1994)

Orthogonal polynomials, Padé approximations and A-stability. - John C. Butcher (Numer. Algorithms, 1996)

DESI Methods for Stiff Initial-Value Problems. - John C. Butcher; Jeff R. Cash; M. T. Diamantakis (ACM Trans. Math. Softw., 1996)

Order and stability of parallel methods for stiff problems. - John C. Butcher (Adv. Comput. Math., 1997)

Nordsieck representation of DIMSIMs. - John C. Butcher; Philippe Chartier; Zdzislaw Jackiewicz (Numer. Algorithms, 1997)

Efficient Runge-Kutta integrators for index-2 differential algebraic equations. - John C. Butcher; Robert P. K. Chan (Math. Comput., 1998)

ARK methods up to order five. - John C. Butcher (Numer. Algorithms, 1998)

DESIRE: diagonally extended singly implicit Runge-Kutta effective order methods. - John C. Butcher; M. T. Diamantakis (Numer. Algorithms, 1998)

The effective order of singly-implicit Runge-Kutta methods. - John C. Butcher; Philippe Chartier (Numer. Algorithms, 1999)

Experiments with a variable-order type 1 DIMSIM code. - John C. Butcher; Philippe Chartier; Zdzislaw Jackiewicz (Numer. Algorithms, 1999)

The McNabb symposium 7-8 February 2000 Auckland, New Zealand. - John C. Butcher (Adv. Decis. Sci., 2000)

Variable stepsize schemes for effective order methods and enhanced order composition methods. - John C. Butcher; T. M. H. Chan (Numer. Algorithms, 2001)

On the implementation of ESIRK methods for stiff IVPs. - John C. Butcher; David Jen Lung Chen (Numer. Algorithms, 2001)

Preface. - John C. Butcher (Numer. Algorithms, 2002)

The A-Stability of Methods with Padé and Generalized Padé Stability Functions. - John C. Butcher (Numer. Algorithms, 2002)

Software Issues for Ordinary Differential Equations. - John C. Butcher (Numer. Algorithms, 2002)

Stability of Numerical Methods for Ordinary Differential Equations. - John C. Butcher; A. D. Heard (Numer. Algorithms, 2002)

Error Estimation for Nordsieck Methods. - John C. Butcher; Zdzislaw Jackiewicz (Numer. Algorithms, 2002)

Nordsieck Methods with an Off-Step Point. - John C. Butcher; A. E. O'Sullivan (Numer. Algorithms, 2002)

Experiments with a New Fifth Order Method. - John C. Butcher; Nicolette Moir (Numer. Algorithms, 2003)

A new approach to error estimation for general linear methods. - John C. Butcher; Zdzislaw Jackiewicz (Numerische Mathematik, 2003)

Construction of General Linear Methods with Runge-Kutta Stability Properties. - John C. Butcher; Zdzislaw Jackiewicz (Numer. Algorithms, 2004)

High Order A-stable Numerical Methods for Stiff Problems. - John C. Butcher (J. Sci. Comput., 2005)

Second derivative methods with RK stability. - John C. Butcher; Gholamreza Hojjati (Numer. Algorithms, 2005)

Similarity solutions of partial differential equations using DESOLV. - K. T. Vu; John C. Butcher; J. Carminati (Comput. Phys. Commun., 2007)

Error propagation of general linear methods for ordinary differential equations. - John C. Butcher; Zdzislaw Jackiewicz; W. M. Wright (J. Complex., 2007)

Runge-Kutta methods. - John C. Butcher (Scholarpedia, 2007)

Numerical methods for ordinary differential equations: early days. - John C. Butcher (The Birth of Numerical Analysis, 2009)

General linear methods for ordinary differential equations. - John C. Butcher (Math. Comput. Simul., 2009)

The existence of symplectic general linear methods. - John C. Butcher; L. L. Hewitt (Numer. Algorithms, 2009)

Trees and numerical methods for ordinary differential equations. - John C. Butcher (Numer. Algorithms, 2010)

Preface. - John C. Butcher; Zdzislaw Jackiewicz; Helmut Podhaisky; Rüdiger Weiner (Numer. Algorithms, 2010)

Polynomial algebra for Birkhoff interpolants. - John C. Butcher; Robert M. Corless; Laureano González-Vega; Azar Shakoori (Numer. Algorithms, 2011)

Runge-Kutta methods and Banach algebras. - John C. Butcher (J. Comput. Appl. Math., 2012)

Predictor-corrector Obreshkov pairs. - John C. Butcher; Pavla Sehnalová (Computing, 2013)

Symplectic effective order methods. - John C. Butcher; Gulshad Imran (Numer. Algorithms, 2014)

The Control of Parasitism in G-symplectic Methods. - John C. Butcher; Yousaf Habib; Adrian T. Hill; Terence J. T. Norton (SIAM J. Numer. Anal., 2014)

The cohesiveness of G-symplectic methods. - John C. Butcher (Numer. Algorithms, 2015)

A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems. - Yuto Miyatake; John C. Butcher (SIAM J. Numer. Anal., 2016)

Trees, Stumps, and Applications. - John C. Butcher (Axioms, 2018)

Variable order and stepsize in general linear methods. - Saghir Ahmad; John C. Butcher; Winston L. Sweatman (Numer. Algorithms, 2019)

Trees and B-series. - John C. Butcher (Numer. Algorithms, 2019)

A New Solution to a Cubic Diophantine Equation. - John C. Butcher (Axioms, 2022)

High-order linearly implicit schemes conserving quadratic invariants. - Shun Sato; Yuto Miyatake; John C. Butcher (CoRR, 2022)

Isomeric trees and the order of Runge-Kutta methods. - John C. Butcher; Helmut Podhaisky (J. Comput. Appl. Math., 2022)

On the B-series composition theorem. - John C. Butcher; Taketomo Mitsui; Yuto Miyatake; Shun Sato (CoRR, 2024)

Featured Review: Numerical Integration of Differential Equations. - John C. Butcher; Robert M. Corless (SIAM Rev., 2025)