On the construction of error estimators for implicit Runge-Kutta methods
When an implicit Runge-Kutta method is applied to a stiff system of ordinary differential equations it is well known that an estimation of the local error which gives realistic estimates for stiff components is rather difficult. The stiff error components may be highly overestimated if the stability function is unbounded at infinity. There are codes improving such inadequate error estimates by premultiplying the estimate by a filter matrix which damps or removes large stiff error components. The authors resolve this problem by introducing an implicit error estimator with the desired properties for stiff components without employing the somewhat arbitrary technique of filter matrix. The proposed error estimator contains a free parameter determining the magnitude of the error; the authors show how this parameter is to be selected on the basis of the method properties. The construction principles for the error estimator can be adapted to all implicit Runge-Kutta methods. For details the reader is referred to the interesting note.
scientific article; zbMATH DE number 1115942