Construction of starting algorithms for the RK-Gauss methods

In this paper starting algorithms for the numerical solution of stage equations in Runge-Kutta-Gauss formulae with 2, 3 and 4 stages are constructed. For each of these formulae, three types of starting algorithms are given according to their requirement of none, one or two additional function evaluations per step. Numerical experiments with Hamiltonian systems are presented to show the superior performance of the new starting algorithms of high order.