J. C. Butcher

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All published works

Action	Title	Year	Authors
+	<b>Featured Review:</b> Numerical Integration of Differential Equations	2025	J. C. Butcher Robert M. Corless
+ PDF Chat	On the B-series composition theorem	2024	J. C. Butcher Taketomo Mitsui Yuto Miyatake Shun Sato
+	High-order linearly implicit schemes conserving quadratic invariants	2023	Shun Sato Yuto Miyatake J. C. Butcher
+	Isomeric trees and the order of Runge–Kutta methods	2022	J. C. Butcher Helmut Podhaisky
+ PDF Chat	A New Solution to a Cubic Diophantine Equation	2022	J. C. Butcher
+	High-order linearly implicit schemes conserving quadratic invariants	2022	Shunichi Sato Yuto Miyatake J. C. Butcher
+ PDF Chat	Isomeric trees and the order of Runge--Kutta methods	2021	J. C. Butcher Helmut Podhaisky
+	B-series and Runge–Kutta methods	2021	J. C. Butcher
+	Trees and forests	2021	J. C. Butcher
+	Differential equations, numerical methods and algebraic analysis	2021	J. C. Butcher
+	B-Series and Multivalue Methods	2021	J. C. Butcher
+	B-Series and Geometric Integration	2021	J. C. Butcher
+	Isomeric trees and the order of Runge--Kutta methods	2021	J. C. Butcher Helmut Podhaisky
+ PDF Chat	Trees, Stumps, and Applications	2018	J. C. Butcher
+	Partitioned general linear methods for separable Hamiltonian problems	2017	J. C. Butcher Raffaele D’Ambrosio
+	Runge and his legacy	2017	J. C. Butcher
+	Trees, B-series and G-symplectic methods	2017	J. C. Butcher
+	Runge Kutta methods - Theory, algorithmic design and applications in computational engineering and science	2017	J. C. Butcher Andreas Meister Detlef Kuhl
+	Sensitivity of modified Patankar-type schemes for systems of conservative production-destruction equations	2017	Andreas Meister J. C. Butcher
+	A G-symplectic method with order 6	2016	J. C. Butcher Gulshad Imran Helmut Podhaisky
+	Numerical Methods for Ordinary Differential Equations	2016	J. C. Butcher
+	Runge–Kutta Methods	2016	J. C. Butcher
+	References	2016	J. C. Butcher
+	General Linear Methods	2016	J. C. Butcher
+	Numerical Differential Equation Methods	2016	J. C. Butcher
+	Linear Multistep Methods	2016	J. C. Butcher
+	Index	2016	J. C. Butcher
+ PDF Chat	Symmetric general linear methods	2016	J. C. Butcher Adrian T. Hill Terence Norton
+ PDF Chat	A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems	2016	Yuto Miyatake J. C. Butcher
+	Counting Trees and Rooted Trees with Applications	2016	J. C. Butcher
+	Symmetric general linear methods	2015	J. C. Butcher Adrian T. Hill Terrence Norton
+	The cohesiveness of G-symplectic methods	2015	J. C. Butcher
+	Order conditions for G-symplectic methods	2015	J. C. Butcher Gulshad Imran
+	Algebraic analysis of structure-preserving general linear methods	2015	J. C. Butcher
+	Runge–Kutta Methods for Ordinary Differential Equations	2015	J. C. Butcher
+	Gauss Methods	2015	J. C. Butcher
+	Symmetric general linear methods	2015	J. C. Butcher Adrian V. S. Hill Terrence Norton
+ PDF Chat	The Control of Parasitism in $G$-symplectic Methods	2014	J. C. Butcher Yousaf Habib Adrian T. Hill Terence Norton
+	Symplectic effective order methods	2013	J. C. Butcher Gulshad Imran
+	Ordinary differential equations	2013	J. C. Butcher
+	Predictor–corrector Obreshkov pairs	2013	J. C. Butcher Pavla Sehnalová
+	Dealing with Parasitic Behaviour in G-Symplectic Integrators	2012	J. C. Butcher
+	Runge–Kutta methods and Banach algebras	2012	J. C. Butcher
+	Applications of order arrows	2012	Ali Abdi J. C. Butcher
+	Order bounds for second derivative approximations	2011	Ali Abdi J. C. Butcher
+	The tree and forest spaces with applications to initial-value problem methods	2010	J. C. Butcher T. M. H. Chan
+	Polynomial algebra for Birkhoff interpolants	2010	J. C. Butcher Robert M. Corless Laureano González-Vega Azar Shakoori
+	Practical Runge--Kutta methods for scientific computation	2009	J. C. Butcher
+	Numerical methods for ordinary differential equations: early days	2009	J. C. Butcher
+	Trees, B-series and exponential integrators	2009	J. C. Butcher
+ PDF Chat	PRACTICAL RUNGE–KUTTA METHODS FOR SCIENTIFIC COMPUTATION	2009	J. C. Butcher
+	The existence of symplectic general linear methods	2008	J. C. Butcher L. L. Hewitt
+	Order and stability of generalized Padé approximations	2008	J. C. Butcher
+	Numerical Differential Equation Methods	2008	J. C. Butcher
+	References	2008	J. C. Butcher
+	Numerical Methods for Ordinary Differential Equations	2008	J. C. Butcher
+ PDF Chat	Forty‐five years of A‐stability	2008	J. C. Butcher
+	Similarity solutions of partial differential equations using DESOLV	2007	Khai T. Vu J. C. Butcher J. Carminati
+	Error propagation of general linear methods for ordinary differential equations	2007	J. C. Butcher Z. Jackiewicz William M. D. Wright
+	General linear methods for ordinary differential equations	2007	J. C. Butcher
+	Runge-Kutta methods	2007	J. C. Butcher
+	Thirty years of G-stability	2006	J. C. Butcher
+	General linear methods	2006	J. C. Butcher
+	Linear Multistep Methods as Irreducible General Linear Methods	2006	J. C. Butcher Adrian T. Hill
+	High order A-stable numerical methods for stiff problems	2005	J. C. Butcher
+	High Order A-stable Numerical Methods for Stiff Problems	2005	J. C. Butcher
+	On error estimation in general linear methods for stiff ODEs	2005	J. C. Butcher Helmut Podhaisky
+	Applications of doubly companion matrices	2005	J. C. Butcher William M. D. Wright
+	ARK methods for stiff problems	2004	J. C. Butcher Nicolette Rattenbury
+	Unconditionally Stable General Linear Methods for Ordinary Differential Equations	2004	J. C. Butcher Z. Jackiewicz
+	The Construction of Practical General Linear Methods	2003	J. C. Butcher William M. D. Wright
+	A new approach to error estimation for general linear methods	2003	J. C. Butcher Z. Jackiewicz
+	A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations	2003	J. C. Butcher J. Carminati Khai T. Vu
+	Numerical Methods for Ordinary Differential Equations	2003	J. C. Butcher
+	Numerical Differential Equation Methods	2003	J. C. Butcher
+	A transformation relating explicit and diagonally-implicit general linear methods	2003	J. C. Butcher William M. D. Wright
+	None	2003	J. C. Butcher Nicolette Moir
+	A New Approach to the Algebraic Structures for Integration Methods	2002	J. C. Butcher T. M. H. Chan
+	None	2002	J. C. Butcher Z. Jackiewicz
+	None	2001	J. C. Butcher
+	None	2001	J. C. Butcher Z. Jackiewicz
+	Numerical methods for ordinary differential equations in the 20th century	2000	J. C. Butcher
+	A new type of singly-implicit Runge–Kutta method	2000	J. C. Butcher D.J.L. Chen
+	Multi-step zero approximations for stepsize control	2000	J. C. Butcher T. M. H. Chan
+	The choice of parameters in parallel general linear methods for stiff problems	2000	J. C. Butcher A.D. Singh
+	Experience of STRIDE applied to delay differential equations	2000	Christopher Baker J. C. Butcher
+	None	1999	J. C. Butcher P. Chartier
+	ESIRK methods and variable stepsize	1998	J. C. Butcher D. J. L. Chen
+	Order and effective order	1998	J. C. Butcher
+	Construction of high order diagonally implicit multistage integration methods for ordinary differential equations	1998	J. C. Butcher Z. Jackiewicz
+	None	1998	J. C. Butcher
+ PDF Chat	Efficient Runge-Kutta integrators for index-2 differential algebraic equations	1998	J. C. Butcher Raymond H. Chan
+	Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations	1997	J. C. Butcher Z. Jackiewicz
+	Order conditions for Two-Step Runge-Kutta methods	1997	J. C. Butcher S. Tracogna
+	A generalization of singly-implicit Runge-Kutta methods	1997	J. C. Butcher P. Chartier
+	An introduction to “Almost Runge-Kutta” methods	1997	J. C. Butcher
+	A nonlinear optimization approach to the construction of general linear methods of high order	1997	J. C. Butcher Z. Jackiewicz Hans D. Mittelmann
+	None	1997	J. C. Butcher P. Chartier Z. Jackiewicz
+	None	1997	J. C. Butcher
+	Orthogonal polynomials, Padé approximations and A-stability	1996	J. C. Butcher
+ PDF Chat	DESI methods for stiff initial-value problems	1996	J. C. Butcher J. R. Cash Michail Diamantakis
+	Runge-Kutta methods: some historical notes	1996	J. C. Butcher Gerhard Wanner
+	The number of conditions for a Runge-Kutta method to have effective order p	1996	J. C. Butcher J. M. Sanz‐Serna
+	Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations	1996	J. C. Butcher Z. Jackiewicz
+	A history of Runge-Kutta methods	1996	J. C. Butcher
+	General linear methods	1996	J. C. Butcher
+	Parallel general linear methods for stiff ordinary differential and differential algebraic equations	1995	J. C. Butcher P. Chartier
+	Numerical Solution of Ordinary Differential Equations.	1995	J. C. Butcher L. F. Shampine
+	On fifth order Runge-Kutta methods	1995	J. C. Butcher
+ PDF Chat	Defect Correction for Two-Point Boundary Value Problems on Nonequidistant Meshes	1995	J. C. Butcher J. R. Cash Gerald Moore Robert D. Russell
+	Initial value problems: numerical methods and mathematics	1994	J. C. Butcher
+	Runge–Kutta Methods in Modern Computation, Part I: Fundamental Concepts	1994	J. C. Butcher
+	A transformation for the analysis of DIMSIMs	1994	J. C. Butcher
+	The Parallel Solution of Ordinary Differential Equations and Some Special Functions	1994	J. C. Butcher
+	Diagonally implicit general linear methods for ordinary differential equations	1993	J. C. Butcher Z. Jackiewicz
+	General linear methods for the parallel solution of ordinary differential equations	1993	J. C. Butcher
+	Estimating local truncation errors for Runge-Kutta methods	1993	J. C. Butcher P.B. Johnston
+	Diagonally-implicit multi-stage integration methods	1993	J. C. Butcher
+	The role of orthogonal polynomials in numerical ordinary differential equations	1992	J. C. Butcher
+	Generalized Padé approximations to the exponential function	1992	J. C. Butcher F. H. Chipman
+	On symmetrizers for Gauss methods	1991	J. C. Butcher R. P. K. Chan
+	Towards Efficient Runge–Kutta Methods for Stiff Systems	1990	J. C. Butcher J. R. Cash
+	Some recent developments on numerical initial value problems: a survey	1989	J. C. Butcher J. R. Cash
+	The Numerical Analysis of Ordinary Differential Equations; Runge-Kutta and General Linear Methods.	1988	Kenneth R. Jackson J. C. Butcher
+	On a class of matrices with real eigenvalues	1988	J. C. Butcher
+ PDF Chat	Towards efficient implementation of singly-implicit methods	1988	J. C. Butcher
+	The equivalence of algebraic stability andAN-stability	1987	J. C. Butcher
+	Linear and non-linear stability for general linear methods	1987	J. C. Butcher
+	On Sequences of Imbedded Integration Rules	1987	Philip Rabinowitz Jaroslav Kautský Sylvan Elhay J. C. Butcher
+	The non-existence of ten stage eighth order explicit Runge-Kutta methods	1985	J. C. Butcher
+	General linear method: a survey	1985	J. C. Butcher
+	An application of the runge-kutta space	1984	J. C. Butcher
+	An Iteration Scheme for Implicit Runge—Kutta Methods	1983	G. J. Cooper J. C. Butcher
+	A short proof concerningB-stability	1982	J. C. Butcher
+	A generalization of singly-implicit methods	1981	J. C. Butcher
+	Stability Properties for a General Class of Methods for Ordinary Differential Equations	1981	J. C. Butcher
+	An implementation of singly-implicit Runge-Kutta methods	1980	Kevin Burrage J. C. Butcher F. H. Chipman
+	Non-linear stability of a general class of differential equation methods	1980	Kevin Burrage J. C. Butcher
+	Some implementation schemes for implicit Runge-Kutta methods	1980	J. C. Butcher
+	Stability Criteria for Implicit Runge–Kutta Methods	1979	Kevin Burrage J. C. Butcher
+	OnA-stable implicit Runge-Kutta methods	1977	J. C. Butcher
+	On the implementation of implicit Runge-Kutta methods	1976	J. C. Butcher
+	A class of implicit methods for ordinary differential equations	1976	J. C. Butcher
+	A stability property of implicit Runge-Kutta methods	1975	J. C. Butcher
+	An Order Bound for Runge–Kutta Methods	1975	J. C. Butcher
+	The order of differential equation methods	1974	J. C. Butcher
+	Order Conditions for General Linear Methods for Ordinary Differential Equations	1974	J. C. Butcher
+ PDF Chat	The order of numerical methods for ordinary differential equations	1973	J. C. Butcher
+	On step control criteria	1973	J. C. Butcher
+ PDF Chat	An algebraic theory of integration methods	1972	J. C. Butcher
+ PDF Chat	A convergence criterion for a class of integration methods	1972	J. C. Butcher
+	The order of differential equation methods.	1972	J. C. Butcher
+ PDF Chat	An Algebraic Theory of Integration Methods	1972	J. C. Butcher
+	A Spectrum of mathematics : essays presented to H. G. Forder	1971	H. G. Forder J. C. Butcher
+	The effective order of Runge-Kutta methods	1969	J. C. Butcher
+ PDF Chat	A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages	1967	J. C. Butcher
+ PDF Chat	On the convergence of numerical solutions to ordinary differential equations	1966	J. C. Butcher
+ PDF Chat	On the Convergence of Numerical Solutions to Ordinary Differential Equations	1966	J. C. Butcher
+ PDF Chat	On the Attainable Order of Runge-Kutta Methods	1965	J. C. Butcher
+	Tables of Coefficients for Implicit Runge-Kutta Processes	1965	Anthony Ralston J. C. Butcher
+ PDF Chat	A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations	1965	J. C. Butcher
+ PDF Chat	On the attainable order of Runge-Kutta methods	1965	J. C. Butcher
+ PDF Chat	On Runge-Kutta processes of high order	1964	J. C. Butcher
+ PDF Chat	Integration processes based on Radau quadrature formulas	1964	J. C. Butcher
+ PDF Chat	Implicit Runge-Kutta Processes	1964	J. C. Butcher
+ PDF Chat	On the integration processes of A. Huťa	1963	J. C. Butcher
+ PDF Chat	Coefficients for the study of Runge-Kutta integration processes	1963	J. C. Butcher
+ PDF Chat	A partition test for pseudo-random numbers	1961	J. C. Butcher
+	Numerical calculations on the new approach to the cascade theory - III	1958	S. K. Srinivasan J. C. Butcher B. A. Chartres H. Messel

Common Coauthors

Coauthor	Papers Together
Z. Jackiewicz	11
Helmut Podhaisky	5
J. R. Cash	4
William M. D. Wright	4
Yuto Miyatake	4
P. Chartier	4
Adrian T. Hill	4
Gulshad Imran	3
T. M. H. Chan	3
Kevin Burrage	3
J. Carminati	2
Ali Abdi	2
Shun Sato	2
Khai T. Vu	2
Andreas Meister	2
Robert M. Corless	2
Terrence Norton	2
F. H. Chipman	2
Terence Norton	2
Nicolette Rattenbury	1
H. G. Forder	1
Shunichi Sato	1
Yousaf Habib	1
Laura L Hewitt	1
Gerald Moore	1
Jaroslav Kautský	1
S. Tracogna	1
Anthony Ralston	1
D.J.L. Chen	1
P.B. Johnston	1
Christopher Baker	1
Raffaele D’Ambrosio	1
Philip Rabinowitz	1
A.D. Singh	1
S. K. Srinivasan	1
L. F. Shampine	1
R. P. K. Chan	1
Taketomo Mitsui	1
H. Messel	1
Nicolette Moir	1
Kenneth R. Jackson	1
Raymond H. Chan	1
Azar Shakoori	1
Pavla Sehnalová	1
Detlef Kuhl	1
Sylvan Elhay	1
Adrian V. S. Hill	1
Gerhard Wanner	1
Michail Diamantakis	1
B. A. Chartres	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	An algebraic theory of integration methods	1972	J. C. Butcher	23
+	Diagonally-implicit multi-stage integration methods	1993	J. C. Butcher	23
+ PDF Chat	Coefficients for the study of Runge-Kutta integration processes	1963	J. C. Butcher	22
+	The Numerical Analysis of Ordinary Differential Equations; Runge-Kutta and General Linear Methods.	1988	Kenneth R. Jackson J. C. Butcher	20
+ PDF Chat	On the convergence of numerical solutions to ordinary differential equations	1966	J. C. Butcher	20
+ PDF Chat	Solving ordinary differential equations I. nonstiff problems	1987	Ernst Hairer Syvert P. Nørsett Gerhard Wanner	19
+	Numerical Methods for Ordinary Differential Equations	2016	J. C. Butcher	19
+	A special family of Runge-Kutta methods for solving stiff differential equations	1978	Kevin Burrage	18
+	On the Butcher group and general multi-value methods	1974	E. Hairer Gerhard Wanner	17
+	Solving Ordinary Differential Equations II: Stiff and Differential - Algebraic Problems	1991	Ernst Hairer Gerhard Wanner	17
+	Non-linear stability of a general class of differential equation methods	1980	Kevin Burrage J. C. Butcher	16
+	An implementation of singly-implicit Runge-Kutta methods	1980	Kevin Burrage J. C. Butcher F. H. Chipman	15
+	Numerical Methods for Ordinary Differential Equations	2008	J. C. Butcher	15
+	Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s	1977	Roger Alexander	14
+	Runge-kutta schemes for Hamiltonian systems	1988	J. M. Sanz‐Serna	13
+	Beitrag zur Naherungsweisen Integration Totaler Differentialgleichungen	1901	W. Kutta	13
+	On the implementation of implicit Runge-Kutta methods	1976	J. C. Butcher	13
+ PDF Chat	Convergence and stability in the numerical integration of ordinary differential equations	1956	Germund Dahlquist	12
+	G-stability is equivalent toA-stability	1978	Germund Dahlquist	12
+	Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations	2009	Ernst Hairer Christian Lubich Gerhard Wanner	12
+	Discrete Variable Methods in Ordinary Differential Equations.	1962	A. B. Farnell Peter Henrici	12
+	Solving Ordinary Differential Equations II	1996	Ernst Hairer Gerhard Wanner	12
+	The effective order of Runge-Kutta methods	1969	J. C. Butcher	12
+ PDF Chat	Generalized Multistep Predictor-Corrector Methods	1964	William B. Gragg Hans J. Stetter	12
+	Order stars and stability theorems	1978	Gerhard Wanner Ernst Hairer Syvert P. Nørsett	12
+	Towards Efficient Runge–Kutta Methods for Stiff Systems	1990	J. C. Butcher J. R. Cash	11
+	Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations	1997	J. C. Butcher Z. Jackiewicz	11
+ PDF Chat	Ueber die numerische Aufl�sung von Differentialgleichungen	1895	Christopher Runge	11
+	A generalization of singly-implicit Runge-Kutta methods	1997	J. C. Butcher P. Chartier	10
+	The numerical analysis of ordinary differential equations	1987		10
+	Stability Criteria for Implicit Runge–Kutta Methods	1979	Kevin Burrage J. C. Butcher	10
+	General linear methods	2006	J. C. Butcher	10
+	Numerical Hamiltonian Problems	1994	J. M. Sanz‐Serna M. P. Calvo	10
+ PDF Chat	On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations	1974	A. Prothero A. Robinson	10
+	A special stability problem for linear multistep methods	1963	Germund Dahlquist	10
+	Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations	1996	J. C. Butcher Z. Jackiewicz	10
+ PDF Chat	The order of numerical methods for ordinary differential equations	1973	J. C. Butcher	9
+	The Concept of B-Convergence	1981	Reinhard Frank J. Schneid Christoph W. Ueberhuber	9
+	Order Conditions for Canonical Runge–Kutta Schemes	1991	J. M. Sanz‐Serna L.M. Abia	9
+ PDF Chat	On numerical integration of ordinary differential equations	1962	Arnold Nordsieck	9
+	Diagonally implicit general linear methods for ordinary differential equations	1993	J. C. Butcher Z. Jackiewicz	9
+	A stability property of implicit Runge-Kutta methods	1975	J. C. Butcher	9
+	Canonical Runge-Kutta methods	1988	F. M. Lasagni	9
+ PDF Chat	The Control of Parasitism in $G$-symplectic Methods	2014	J. C. Butcher Yousaf Habib Adrian T. Hill Terence Norton	9
+ PDF Chat	A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations	1965	J. C. Butcher	9
+	Error analysis for a class of methods for stiff non-linear initial value problems	1976	Germund Dahlquist	9
+	The Construction of Practical General Linear Methods	2003	J. C. Butcher William M. D. Wright	9
+	Hybrid Methods for Initial Value Problems in Ordinary Differential Equations	1965	C. W. Gear	9
+	<i>A</i>-Stable Methods and Padé Approximations to the Exponential	1973	Byron L. Ehle	8
+	General linear methods: connection to one step methods and invariant curves	1993	Daniel Stoffer	8