Elements of a general theory of composite integration methods
The author reviews his own work on a theory of general linear methods for the numerical integration of ordinary differential equations. The first part deals with the concept of stability and the relation between the order of convergence and the local discretization errors. Various results appear as easy consequences of the theory. The second part treats Runge- Kutta methods within this general framework. The approach gives a recursive scheme for determining the order conditions. The format differs from that obtained using elementary differentials and is of interest. This theory of general linear methods offers a valuable alternative to that developed by \textit{J. C. Butcher} [The numerical analysis of ordinary differential equations, Runge-Kutta and general linear methods (1987; Zbl 0616.65072)].
scientific article; zbMATH DE number 4117767
scientific article