Almost Runge-Kutta methods are a special type of general linear method whose properties closely resemble those of Runge-Kutta methods. However, they have the advantage of higher stage order and the possiblity of efficient interpolation and error-estimation. A brief introduction to ARK methods will be given, including an analysis of the local truncation error. Even though the detailed order conditions are different from those of Runge-Kutta methods, they both make use of rooted trees and elementary differentials. By allowing the number of stages to exceed the order, opportunities exist for optimising the method. This idea will be briefly explored.

MINISIMPOSIUM SESSION: 6. Novel methods for ODEs