I am John Butcher of Auckland, New Zealand.
I was Professor of Mathematics at the University of Auckland from 1966 to 1998.
I then retired as Emeritus Professor.
I am attempting to remain active in research.
Numerical methods for the solution of ordinary differential equations (section 65L in Mathematical Reviews).
Within this broad area I work mainly on multistage methods for initial value problems, such as Runge-Kutta and general linear methods.
Recently a new type of method has been discovered in which the stability is identical with that of a Runge-Kutta method. These are known as IRKS methods (methods possessing "Inherent Runge-Kutta stability".
Order stars are well-known as theoretical tools for investigating and resolving stability questions. Recently "order arrows" have been introduced as an additional method for carrying out similar tasks. The main success is the resolution of the "Butcher-Chipman conjecture" which is now known to be true.
I have become interested in G-symplectic general linear methods. These have some of the properties and behaviour of symplectic Runge-Kutta methods.
At the present time, information is being shared, and in some cases duplicated between this site and my site at the University of Auckland.