Global Error Estimation with Runge--Kutta Methods II

An analysis of global error estimation using the Zadunaiskytechnique with Runge—Kutta methods is presented. Threeforms of interpolant which can lead to valid asymptotic estimationare considered. Test results indicate that the Hermite formcoupled with special Runge—Kutta formulae is to be preferred,particularly when two-term global error estimation can be obtained.Very reliable estimation can be achieved and it is suggestedthat the technique could form the basis of a production code.