B-convergence of general linear methods for stiff problems. (Q1410605)

The concept of B-convergence, originally defined for Runge-Kutta methods by \textit{R. Frank, J. Schneid} and \textit{C. W. Ueberhuber} [SIAM J. Numer. Anal. 18, 753--780 (1981; Zbl 0467.65032)], is extended to general linear methods. It is shown that algebraic stability [cf. \textit{K. Burrage} and \textit{J. C. Butcher} [BIT 20, 185--203 (1980; Zbl 0431.65051)], which together with strict stability at infinity implies B-convergence in this situation is shown to be equal to the generalized stage-order of \textit{S. Li} [J. Comput. Appl. Math. 28, 281--296 (1989; Zbl 0693.65043)]. The results are applied to the special class of multistep Runge-Kutta methods.