RUNGE-KUTTA METHODS - SOME HISTORICAL NOTES

This centenary history of Runge-Kutta methods contains an appreciation of the early work of Runge, Heun, Kutta, and Nystrom and a survey of some significant developments of these methods over the last hundred y ears. In particular, the order conditions, as they are now understood, will be outlined, as will the introduction and practical implementati on of implicit Runge-Kutta methods, the use of linear and nonlinear st ability analysis in the assessment of Runge-Kutta methods, and the the ory and applications of the composition of methods. Of the many furthe r developments that have arisen, most are discussed only briefly; howe ver, the recent interest in Runge-Kutta methods for Hamiltonian system s will be surveyed in more detail.