| 多步Runge-Kutta方法的保单调性 |
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| 引用本文： | 甘四清,史可.多步Runge-Kutta方法的保单调性[J].计算数学,2010,32(3):247-264. |
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| 作者姓名： | 甘四清 史可 |
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| 作者单位： | 中南大学数学科学与计算技术学院,长沙,410075 |
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| 基金项目： | 国家自然科学基金(10871207)和教育部留学回国人员科研启动基金资助项目 |
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| 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.
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| 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 |
| 收稿时间： | 2007-07-08 |
| 修稿时间： | 2009-12-11 |
MONOTONICITY-PRESERVING MULTISTEP RUNGE-KUTTA METHODS |
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| Gan Siqing,Shi Ke.MONOTONICITY-PRESERVING MULTISTEP RUNGE-KUTTA METHODS[J].Mathematica Numerica Sinica,2010,32(3):247-264. |
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| Authors: | Gan Siqing Shi Ke |
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| Institution: | School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, China |
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| Abstract: | 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.
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