# Welcome

**Welcome to the homepage of John Butcher of Auckland, New Zealand.**

**I am a mathematician specializing in numerical analysis.**

### Short biography

- Born in Auckland, New Zealand
- Educated at various primary schools in Auckland and in Dargaville primary school
- Secondary education at Dargaville DHS, Taumarunui DHS and Hamilton HS
- Tertiary education at Auckland University College and University of Sydney. BSc and MSc (Auckland); PhD and DSc (Sydney)
- academic and research positions at Sydney and Canterbury Universities and Stanford Linear Accelerator Center
- Professor of Mathematics, University of Auckland 1966 - 1998
- Emeritus Professor 1999 - present

### Research Interests

#### Ordinary differential equations

Numerical methods for the solution of ordinary differential equations (section 65L in Mathematical Reviews). \[ \frac{d y}{d x} = f(y) \] Within this broad area I work on a number of specialities some of which are listed below.##### Runge-Kutta methods

\[ \begin{array}{c|cccc} c_1 & a_{11} & a_{12} & \cdots & a_{1s}\\ c_2 & a_{21} & a_{22} & \cdots & a_{2s}\\ \vdots & \vdots &\vdots & &\vdots \\ c_s & a_{s1} & a_{s2} & \cdots & a_{ss}\\ \hline & b_1 & b_2 & \cdots & b_s \end{array} \]##### General linear methods

\[ \begin{bmatrix} A & U\\ B & V \end{bmatrix} \]##### G-symplectic general linear methods

\[ \begin{bmatrix} DA + A^{\sf T} D - B ^{\sf T} G B & DU - B^{\sf T} G V\\ U^{\sf T}D - V^{\sf T} G B & G - V^{\sf T} G V \end{bmatrix}=0. \]##### B-series

### Honours and awards

- Fellow Royal Society of New Zealand, 1980
- New Zealand Mathematical Society, Research Award
- Hector Medal, RSNZ, 1996
- Life Member, NZMS, 1998
- Fellow, NZMS, 1999
- ICCMSE Prize for Computational Mathematics, 2003
- Honorary Fellowship: European Society of Computational and Applied Mathematics, 2008
- Fellow, Society for Industrial and Applied Mathematics, 2010
- Jones Medal, Royal Society of New Zealand, 2010
- van Wijngaarden Award, 2011
- Officer of the New Zealand Order of Merit, 2013

### Travel and conferences 2015

#### ICIAM

Beijing, 10-14 August 2015

Contributed paper: "On fifth order Runge-Kutta methods"

#### ICREM7

Kuala Lumpur, 28 August 2015

Invited paper: "Counting trees and rooted trees with applications"

Invited workshop: "B-series for the analysis of numerical methods"

#### Universiti Putra Malaysia

Putra Jaya, 17-28 August 2015

Three lectures on Runge-Kutta methods (17 - 19 August)

Seminar (28 August): "Solving evolutionary problems stably and conservatively"

#### Runge-Kutta workshop

Kassel, 31 August 31 - 2 September 2015

Invited presentations: “Survey of Runge-Kutta Methods“, "Runge-Kutta Methods for Non-Stiff Problems", "Runge-Kutta Methods for Stiff Problems", "Runge-Kutta Methods for Hamiltonian Problems"

#### Humboldt Universiät zu Berlin

Berlin, 4 September 2015:

Seminar "B-series and the order of general linear methods"

#### NUMDIFF

Halle, 7-11 September 2015

Contributed paper within Minisymposium in honour of R. März: “Constructing high order G-symplectic methods“

#### SciCADE

Potsdam, 14-18 September 2015

Contributed paper: “The cohesiveness of G-symplectic methods“

#### Universiät Kassel

Kassel 21 - 23 September 2015:

Seminar "B-series for the analysis of numerical methods"

#### New Zealand Mathematical Society Colloquium

Christchurch 1 - 3 Decembet 2015:

Contributed paper "The construction of high order G-symplectic methods"

#### AUT Mathematical Sciences Symposium

Christchurch 7 - 8 Decembet 2015:

Contributed paper "Speeding up calculations"

### Travel and conferences 2016

#### ICNAAM CONFERENCE

Rhodes, Greece, 19 - 25 September 2016:

Invited paper ”Trees, B-series and G-symplectic methods”,

#### Seminar ETH

Zürich, 28 September 2016:

Lecture ”The construction of high order G-symplectic methods”

#### Conference on Geometric Integration

La Trobe University, 5-7 December 2016:

Lecture ”The construction of high order G-symplectic methods”

### Travel and conferences 2019

#### SciCADE19

Innsbruck, Austria, 22 - 26 July 2019:

Invited paper ”45 years of B-series”,