Secondary nonlinear stability of general linear methods for stiff initial value problems

In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods which is based on two slightly different test problems, and obtained the algebraic conditions that guarantee new stability properties. In this paper, we extend these results to general linear methods and to more general problem class K
στ
The concepts of (k, p, q)-secondary stability and(k, p, q)
^∗
-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraic stability conditions while retaining the virtues of a nonlinear test problem.