Global Error Estimation with Runge—Kutta Methods II

An analysis of global error estimation using the Zadunaisky technique with Runge—Kutta methods is presented. Three forms of interpolant which can lead to valid asymptotic estimation are considered. Test results indicate that the Hermite form coupled 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 suggested that the technique could form the basis of a production code.