THE RELATION BETWEEN LINEAR AND NONLINEAR STABILITY OF GENERAL LINEAR METHODS
一般线性方法的线性与非线性稳定性间的关系

Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit methods. Our results characterize the interrelation between linear and nonlinear stability so that new evidence for the construction of efficient and stable methods is offered.