2026 John C. Butcher: Mathematics Researcher – H-Index, Publications & Awards

Discipline name	D-Index	World Ranking	Current World Ranking	National Ranking	Current National Ranking	Publications	Citations
Mathematics	41	1846	1611	7	7	185	17706

Discipline name

D-Index

World Ranking

Current World Ranking

National Ranking

Current National Ranking

Publications

Citations

Mathematics

1846

1611

185

17706

Research.com Recognitions

2010 - SIAM Fellow For developing the foundations of the modern theory of Runge-Kutta methods.

Overview

John C. Butcher is affiliated with the University of Auckland in New Zealand. Their research is primarily concentrated in the field of Mathematics, with particular emphasis on Numerical Analysis, Computational Mechanics, Algebra and Number Theory, Statistical and Nonlinear Physics, and Computational Theory and Mathematics.

The main topics of their academic work include:

Numerical methods for differential equations
Advanced Numerical Methods in Computational Mathematics
Differential Equations and Numerical Methods
Matrix Theory and Algorithms
Electromagnetic Simulation and Numerical Methods
Injury Epidemiology and Prevention
Urban Transport and Accessibility

Among their recent papers are:

High-order linearly implicit schemes conserving quadratic invariants (2023), published in Applied Numerical Mathematics
Promoting the independent mobility of young people with SEND: The lived experience of young people with autism, ADHD, and learning disabilities (2022), Journal of Transport & Health
Promoting the Independent Mobility of Young People with Special Educational Needs and Disabilities (2022), Journal of Transport & Health
A New Solution to a Cubic Diophantine Equation (2022), Axioms
DIGITAL POVERTY AS A BARRIER TO ACCESS (2023), INTED proceedings

Frequently collaborating co-authors include Yuto Miyatake, Shun Sato, Sarah O'Toole, Rob Webster, and Nicola Christie.

The researcher has published in several venues, with multiple works appearing in Widening Participation and Lifelong Learning, Journal of Transport & Health, and arXiv (Cornell University). Other publication venues include Applied Numerical Mathematics and Axioms.

John C. Butcher has authored book publications with Springer Nature, notably the book titled B-Series published in 2021.

Recognition for their contributions includes being named a SIAM Fellow in 2010 for developing the foundations of the modern theory of Runge-Kutta methods.

Best Publications

Numerical methods for ordinary differential equations

John C. Butcher

5161
Citations
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

J. C. Butcher

1548
Citations
The numerical analysis of ordinary differential equations

John C. Butcher

1064
Citations
Implicit Runge-Kutta processes

J. C. Butcher

1020
Citations
Coefficients for the study of Runge-Kutta integration processes

J. C. Butcher

636
Citations
Numerical Solution of Ordinary Differential Equations.

Unknown

512
Citations
A history of Runge-Kutta methods

J. C. Butcher

473
Citations
On Runge-Kutta processes of high order

J. C. Butcher

461
Citations
Stability Criteria for Implicit Runge–Kutta Methods

Kevin Burrage;J. C. Butcher

413
Citations
An algebraic theory of integration methods

J. C. Butcher

360
Citations
Non-linear stability of a general class of differential equation methods

Kevin Burrage;J. C. Butcher

349
Citations
A Modified Multistep Method for the Numerical Integration of Ordinary Differential Equations

J. C. Butcher

330
Citations
On the implementation of implicit Runge-Kutta methods

J. C. Butcher

313
Citations
Numerical methods for ordinary differential equations in the 20th century

J. C. Butcher

298
Citations
General Linear Methods for Ordinary Differential Equations

John Butcher

286
Citations
On the Convergence of Numerical Solutions to Ordinary Differential Equations

J. C. Butcher

258
Citations
A stability property of implicit Runge-Kutta methods

J. C. Butcher

253
Citations
Runge-Kutta methods: some historical notes

J. C. Butcher;G. Wanner

188
Citations
Diagonally-implicit multi-stage integration methods

J. C. Butcher

180
Citations
Integration processes based on Radau quadrature formulas

J. C. Butcher

162
Citations
An implementation of singly-implicit Runge-Kutta methods

K. Burrage;K. Burrage;K. Burrage;J. C. Butcher;J. C. Butcher;J. C. Butcher;F. H. Chipman;F. H. Chipman;F. H. Chipman

157
Citations

Frequent Co-Authors

Zdzislaw Jackiewicz Arizona State University

Kevin Burrage Queensland University of Technology

Jesús María Sanz-Serna Carlos III University of Madrid

Robert M. Corless University of Western Ontario

Lawrence F. Shampine Southern Methodist University

External Links

Wikipedia of John C. Butcher Personal website of John C. Butcher Google Scholar page

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