Starting procedures for general linear methods

摘要

We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q = p. Order conditions for starting procedures based on the generalized Runge-Kutta (RK) are derived using the theory of rooted trees, elementary differentials, and elementary weights, and examples of generalized RK formulas are given up to the order p = 4.