On error estimation in general linear methods for stiff ODEs

This paper studies the estimation of local truncation errors for a family of general linear methods with inherent Runge–Kutta stability. While integrating with a method of order p it is possible not only to estimate the truncation error of this method but also the truncation error of the method of order p+1 asymptotically correctly. Numerical results for a variable stepsize and variable order implementation for stiff ODEs are given.