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Factored two-step Runge-Kutta methods

A class of two-step fourth order implicit Runge-Kutta Methods designed for stiff systems of ODEs has recently been investigated by the author and others. In this paper certain computational aspects of this class of methods are discussed. Similar algorithms which, in particular, exploit any sparseness properties inherent in the Jacobian matrix are considered along with an efficient way of estimating the local truncation error using embedded methods.