Block one-step methods for starting multistep methods (Q1098580)

Runge-Kutta methods are derived which can be used to provide the required number of starting values for multistep methods. Let q be the number of states in the Runge-Kutta process. Then for \(q=3,4,6,9\) methods are derived to provide q-1 extra starting values of orders 2,3,4,5 respectively, which are of orders 3,4,5,6 at any specified point \(a\). The coefficients of the methods are given in terms of \(a\). The motivation for this development is for starting multistep methods with off-step points.