John C. Butcher | Academic Influence

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John C. Butcher

Computer Science

#700

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#721

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#937

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#985

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Computer Science

John C. Butcher's Degrees

PhD Computer Science University of Auckland

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Why Is John C. Butcher Influential?

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According to Wikipedia, John Charles Butcher is a New Zealand mathematician who specialises in numerical methods for the solution of ordinary differential equations. Butcher works on multistage methods for initial value problems, such as Runge-Kutta and general linear methods. The Butcher group and the Butcher tableau are named after him. More recently, he is investigating a new type of method with stability identical to that of a Runge-Kutta method.

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John C. Butcher's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods (1987) (1366)
Numerical methods for ordinary differential equations (2003) (1303)
Implicit Runge-Kutta processes (1964) (644)
The Numerical Analysis of Ordinary Di erential Equa-tions (1986) (503)
Numerical Methods for Ordinary Differential Equations: Butcher/Numerical Methods (2005) (435)
Coefficients for the study of Runge-Kutta integration processes (1963) (395)
An algebraic theory of integration methods (1972) (301)
Stability Criteria for Implicit Runge–Kutta Methods (1979) (285)
On Runge-Kutta processes of high order (1964) (269)
General linear methods for ordinary differential equations (2009) (242)
Non-linear stability of a general class of differential equation methods (1980) (212)
A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations (1965) (209)
A history of Runge-Kutta methods (1996) (190)
Numerical methods for ordinary differential equations in the 20th century (2000) (183)
On the Convergence of Numerical Solutions to Ordinary Differential Equations (1966) (152)
A stability property of implicit Runge-Kutta methods (1975) (152)
On the implementation of implicit Runge-Kutta methods (1976) (134)
Diagonally-implicit multi-stage integration methods (1993) (130)
Integration processes based on Radau quadrature formulas (1964) (105)
Runge-Kutta methods (2007) (100)
The effective order of Runge-Kutta methods (1969) (100)
Runge-Kutta methods: some historical notes (1996) (84)
An implementation of singly-implicit Runge-Kutta methods (1980) (83)
Second derivative methods with RK stability (2005) (83)
Diagonally implicit general linear methods for ordinary differential equations (1993) (80)
Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations (1997) (78)
Electron number distribution in electron-photon showers in air and aluminium absorbers (1960) (77)
The Construction of Practical General Linear Methods (2003) (75)
On the attainable order of Runge-Kutta methods (1965) (75)
Construction of high order diagonally implicit multistage integration methods for ordinary differential equations (1998) (67)
Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations (1996) (64)
A Transformed implicit Runge-Kutta Method (1979) (64)
An Iteration Scheme for Implicit Runge—Kutta Methods (1983) (59)
General linear methods (1996) (56)
A new type of singly-implicit Runge-Kutta method (2000) (52)
A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations (2003) (52)
A Characterization of Energy-Preserving Methods and the Construction of Parallel Integrators for Hamiltonian Systems (2015) (48)
Order conditions for two-step Runge-Kutta methods (1997) (40)
A Multistep Generalization of Runge-Kutta Methods With Four or Five Stages (1967) (40)
Nordsieck representation of DIMSIMs (2004) (39)
General Linear Methods for Stiff Differential Equations (2001) (39)
The Control of Parasitism in G-symplectic Methods (2014) (38)
Construction of General Linear Methods with Runge–Kutta Stability Properties (2004) (37)
Towards efficient Runge-Kutta methods for stiff systems (1990) (35)
Radial and angular distributions of electrons in electron-photon showers in lead and in emulsion absorbers (1962) (35)
An introduction to “almost Runge-Kutta” methods (1997) (34)
Experiments with a variable-order type 1 DIMSIM code (1999) (34)
A nonlinear optimization approach to the construction of general linear methods of high order (1997) (33)
The effective order of singly-implicit Runge-Kutta methods (1999) (33)
The equivalence of algebraic stability andAN-stability (1987) (32)
Trees and numerical methods for ordinary differential equations (2010) (32)
Electron Number Distribution in Electron-Photon Showers (1958) (32)
A new approach to error estimation for general linear methods (2003) (29)
The non-existence of ten stage eighth order explicit Runge-Kutta methods (1985) (29)
ARK methods for stiff problems (2005) (29)
Error propagation of general linear methods for ordinary differential equations (2007) (29)
A generalization of singly-implicit Runge-Kutta methods (1997) (27)
Trees, B-series and exponential integrators (2010) (25)
On error estimation in general linear methods for stiff ODEs (2006) (25)
DESIRE: diagonally extended singly implicit Runge–Kutta effective order methods (1998) (24)
The number of conditions for a Runge-Kutta method to have effective order p (1996) (24)
A Reliable Error Estimation for Diagonally Implicit Multistage Integration Methods (2001) (23)
The existence of symplectic general linear methods (2009) (23)
Numerical Differential Equation Methods (2005) (22)
A generalization of singly-implicit methods (1981) (21)
DESI methods for stiff initial-value problems (1996) (21)
Polynomial algebra for Birkhoff interpolants (2011) (21)
General linear methods for the parallel solution of ordinary differential equations (1993) (21)
Partitioned general linear methods for separable Hamiltonian problems (2017) (21)
Linear and non-linear stability for general linear methods (1987) (20)
Order and stability of generalized Padé approximations (2009) (20)
Parallel general linear methods for stiff ordinary differential and differential algebraic equations (1995) (20)
A transformation relating explicit and diagonally-implicit general linear methods (2003) (19)
Towards efficient implementation of singly-implicit methods (1988) (19)
Similarity solutions of partial differential equations using DESOLV (2007) (19)
Random Sampling from the Normal Distribution (1961) (19)
Some implementation schemes for implicit Runge-Kutta methods (1980) (19)
A transformation for the analysis of DIMSIMs (1994) (18)
Thirty years of G-stability (2006) (18)
The A-Stability of Methods with Padé and Generalized Padé Stability Functions (2002) (18)
The order of numerical methods for ordinary differential equations (1973) (16)
An Order Bound for Runge–Kutta Methods (1975) (16)
Order and effective order (1998) (16)
The role of orthogonal polynomials in numerical ordinary differential equations (1992) (16)
Symmetric general linear methods (2015) (16)
ON FIFTH AND SIXTH ORDER EXPLICIT RUNGE-KUTTA METHODS : ORDER CONDITIONS AND ORDER BARRIERS (16)
Rayleigh Wave Dispersion for a Single Layer on an Elastic Half Space (1960) (16)
Estimating local truncation errors for Runge-Kutta methods (1993) (16)
Runge–Kutta Methods for Ordinary Differential Equations (2015) (15)
Linear Multistep Methods as Irreducible General Linear Methods (2006) (15)
Forty‐five years of A‐stability (2008) (15)
General linear method: a survey (1985) (15)
ESIRK methods and variable stepsize (1998) (15)
Order and stability of parallel methods for stiff problems (1997) (15)
Dealing with Parasitic Behaviour in G-Symplectic Integrators (2013) (15)
High Order A-stable Numerical Methods for Stiff Problems (2005) (15)
Error Estimation for Nordsieck Methods (2002) (14)
On the integration processes of A. Huťa (1963) (14)
Stability of Numerical Methods for Ordinary Differential Equations (2002) (14)
Generalized Padé approximations to the exponential function (1992) (14)
Parallelism in the Numerical Integration of Initial Value Problems. (1995) (14)
Order bounds for second derivative approximations (2012) (14)
The adaptation of STRIDE to delay differential equations (1992) (14)
Applications of doubly companion matrices (2006) (13)
On fifth order Runge-Kutta methods (1995) (13)
A New Approach to the Algebraic Structures for Integration Methods (2002) (13)
An application of the runge-kutta space (1984) (13)
On Sequences of Imbedded Integration Rules (1987) (12)
Defect correction for two-point boundary value problems on nonequidistant meshes (1995) (12)
Unconditionally Stable General Linear Methods for Ordinary Differential Equations (2004) (12)
Order, stepsize and stiffness switching (1990) (12)
OnA-stable implicit Runge-Kutta methods (1977) (11)
Nordsieck Methods with an Off-Step Point (2002) (11)
Stability Properties for a General Class of Methods for Ordinary Differential Equations (1981) (11)
Optimal order and stepsize sequences (1986) (11)
The forces on obstacles suspended in flowing granular materials (1983) (10)
A G-symplectic method with order 6 (2017) (9)
On symmetrizers for Gauss methods (1991) (9)
Efficient Runge-Kutta integrators for index-2 differential algebraic equations (1998) (9)
On the implementation of ESIRK methods for stiff IVPs (2001) (9)
ARK methods up to order five (1998) (9)
Experiments with a New Fifth Order Method (2003) (9)
Experience of STRIDE applied to delay differential equations (2000) (8)
A Modified Approach to Predict Dissolution and Absorption of Polydisperse Powders (2008) (8)
A simulation study of quasi-fixation of genes due to random fluctuation of selection intensities. (1966) (8)
Multi-step zero approximations for stepsize control (2000) (8)
A Spectrum of mathematics : essays presented to H. G. Forder (1971) (8)
Numerical Methods for Differential Equations and Applications (1997) (7)
Predictor–corrector Obreshkov pairs (2013) (7)
Applications of order arrows (2012) (7)
The cohesiveness of G-symplectic methods (2015) (7)
Order conditions for G-symplectic methods (2015) (7)
The tree and forest spaces with applications to initial-value problem methods (2010) (7)
The choice of parameters in parallel general linear methods for stiff problems (2000) (7)
Runge-Kutta methods in modern computation, part I: fundamental concepts (1994) (6)
Numerical methods for ordinary differential equations: early days (2009) (6)
Symplectic effective order methods (2014) (6)
High order A-stable numerical methods for stiff problems (2005) (6)
B-Series (2021) (6)
Practical Runge--Kutta methods for scientific computation (2009) (5)
A convergence criterion for a class of integration methods (1972) (5)
A partition test for pseudo-random numbers (1961) (5)
Order Conditions for General Linear Methods for Ordinary Differential Equations (1974) (4)
TABLES OF AVERAGE NUMBERS FOR ELECTRON-PHOTON SHOWERS AT SMALL DEPTHS OF ABSORBER (1958) (4)
Theory of Difference Equations: Numerical Methods and Applications (V. Lakshmikantham and D. Trigiante) (1989) (4)
Numerical calculations on the new approach to the cascade theory - III (1958) (4)
Variable stepsize schemes for effective order methods and enhanced order composition methods (2001) (4)
Initial value problems: numerical methods and mathematics (1994) (4)
Trees, Stumps, and Applications (2018) (4)
The order of differential equation methods (1974) (4)
The impact of microelectronics technology (1983) (3)
On a class of matrices with real eigenvalues (1988) (3)
Runge–Kutta Methods in Modern Computation, Part II: Implicit Methods and Related Applications (1994) (3)
B‐series and B‐series Coefficients (2009) (3)
The Order of Numerical Methods for Ordinary (1973) (3)
A class of implicit methods for ordinary differential equations (1976) (3)
Some orbital test problems (1994) (2)
Treatment variances for experimental designs with serially correlated observations (1956) (2)
Runge-Kutta methods and Banach algebras (2012) (2)
Differential and Difference Equations (2005) (2)
High-order linearly implicit schemes conserving quadratic invariants (2022) (2)
The Use of Butcher Series in the Analysis of Newton-Like Iterations in Runge-Kutta Formulas (2007) (2)
Sensitivity of modified Patankar-type schemes for systems of conservative production-destruction equations (2017) (2)
RUNGE-KUTTA METHODS AS MATHEMATICAL OBJECTS (1996) (2)
The Parallel Solution of Ordinary Differential Equations and Some Special Functions (1994) (2)
Similarity solutions using DESOLV (2008) (1)
A short proof concerningB-stability (1982) (1)
Ordinary differential equations (2014) (1)
RESULTS ON THE ANGULAR AND RADIAL DISTRIBUTIONS OF PARTICLES IN ELECTRON- PHOTON SHOWERS (1962) (1)
Some recent developments on numerical initial value problems: a survey (1989) (1)
On step control criteria (1973) (1)
Difference Equations from Differential Equations (W. J. Lick) (1992) (1)
Isomeric trees and the order of Runge-Kutta methods (2021) (1)
Software Issues for Ordinary Differential Equations (2002) (1)
B-series and B-series Coefficients 1 (2010) (0)
The McNabb Symposium, 7-8 February 2000, Auckland, New Zealand (2001) (0)
A New Solution to a Cubic Diophantine Equation (2022) (0)
B-Series and Geometric Integration (2021) (0)
Some numerical methods for stiff problems (2003) (0)
Order bounds for second derivative approximations (2011) (0)
Trees and B-series (2018) (0)
Order conditions for G-symplectic methods (2015) (0)
A Convergence Criterion for a Class of (1972) (0)
Algebraic Analysis and Integration Methods (2021) (0)
A G-symplectic method with order 6 (2016) (0)
Accurate and stable time integrators (2009) (0)
B-series and Algebraic Analysis (2021) (0)
Counting Trees and Rooted Trees with Applications (2016) (0)
Predictor–corrector Obreshkov pairs (2013) (0)
Linear Multistep Methods (2005) (0)
A Coin Tossing Problem (Danny Newman) (1978) (0)
Tables of Coefficients for Implicit Runge-Kutta Processes (1965) (0)
Trees, B-series and G-symplectic methods (2017) (0)
Runge Kutta methods - Theory, algorithmic design and applications in computational engineering and science (2017) (0)
The cohesiveness of G-symplectic methods (2015) (0)
B-series and Runge–Kutta methods (2021) (0)
Pin the Convergence of Numerical Solutions to Ordinary Differential Equations' (1965) (0)
Preface (2002) (0)
Ambition, Distraction, Uglification and Derision (2009) (0)
MOS devices - Design and manufacture (1983) (0)
A Seventh Order Method fro the Numerical Solution of Ordinary Differential Equations (1966) (0)
Obituary: Henry George Forder (1985) (0)
Variable order and stepsize in general linear methods (2019) (0)
S Lac -pub-207 a Multistep Generalization of Runge-kutta Methods with 4 or 5 Stages* (0)
B-Series and Multivalue Methods (2021) (0)
Trees and forests (2021) (0)
North-Holland 231 CAM 1251 e role of orthogonal polvnomials in numerical ordinary differeitial equations (2001) (0)
Trees and B-series (2018) (0)
The McNabb symposium 7-8 February 2000 Auckland, New Zealand (2000) (0)
Symmetric general linear methods (2016) (0)
Variable order and stepsize in general linear methods (2019) (0)
Algebraic analysis of structure-preserving general linear methods (2015) (0)
Preface (2009) (0)
Orthogonal polynomials, Padé approximations and A-stability (1996) (0)
Differential equations, numerical methods and algebraic analysis (2021) (0)
UNIVERSITY OF MANCHESTER Experience of STRIDE applied to delay differential equations (2000) (0)
Symplectic effective order methods (2013) (0)

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