多步Runge-Kutta方法的保单调性  

MONOTONICITY-PRESERVING MULTISTEP RUNGE-KUTTA METHODS

作　　者：甘四清[1] 史可[1] 

机构地区：[1]中南大学数学科学与计算技术学院

出　　处：《计算数学》2010年第3期247-264,共18页Mathematica Numerica Sinica

基　　金：国家自然科学基金(10871207);教育部留学回国人员科研启动基金资助项目

摘　　要：一类重要的常微分方程源自用线方法求解非线性双曲型偏微分方程，这类常微分方程的解具有单调性，因此要求数值方法能保持原系统的这种性质．本文研究多步Runge—Kutta方法求解常微分方程初值问题的保单调性．分别获得了多步Runge—Kutta方法是条件单调和无条件单调的充分条件．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 monotonicitv preserving,respectively.

关 键 词：常微分方程初值问题 多步RUNGE-KUTTA方法 单调性 一般线性方法 

分 类 号：O241.8[理学—计算数学]