Regularity properties of general linear methods for initial value problems of ordinary differential equations Original Research Article

The main purpose of the present paper is to examine the asymptotic states of general linear methods for initial value problems of ordinary differential equations, and to extend the existing relevant results of Runge–Kutta methods, linear multistep methods by Humphries (1993) and Stuart and Humphries (1994). In particular, the existence of spurious steady solutions and period-2 solutions in the time step is studied, and the concepts of (strong and weak) R[1] -regularity and (weak) R[2] -regularity of general linear methods are introduced and studied. Some sufficient conditions for (strong and weak) R[1] -regularity and (weak) R[2] -regularity of such methods applied to initial value problems of ordinary differential equations with a globally Lipschitz condition or contractive or monotone condition are given.