Global error estimation with runge-kutta triples

Abstract

The applications of Runge-Kutta (RK) interpolation to global error estimation using the Zadunaisky and related techniques are considered. It is shown that the pseudo-problem can be based on dense output values within any one step and reliable global error estimates can be obtained at the integration mesh-points by using special RK formulae. Some special formulae of orders 2–6 are presented together with numerical results