MONOTONICITY-PRESERVING MULTISTEP RUNGE-KUTTA METHODS
多步Runge-Kutta方法的保单调性

An important class of ordinary system is that whose solutions satisfy a monotonicity property for a given norm. The system arises from the discretization of the spatial derivatives in the hyperbolic partial differential equations. For these problems, a natural requirement for the numerical solution is the reflection of this monotonicity property, perhaps under certain stepsize restriction. This paper deals with the monotonicity property of multistep Runge-Kutta methods. Sufficient conditions are given for multistep Runge-Kutta methods to be conditional monotonicity preserving and unconditional monotonicity preserving, respectively.