[1]侯国屏.Gear法用于二阶线性微分方程组时的稳定性与局部截断误差分析[J].深圳大学学报理工版,1986,(3):34-37.
 Hou Guoping.The Stability and Local Truncation Error in Applying Gear’s Method to Second-Order Differential Equations[J].Journal of Shenzhen University Science and Engineering,1986,(3):34-37.
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Gear法用于二阶线性微分方程组时的稳定性与局部截断误差分析()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
期数:
1986年3期
页码:
34-37
栏目:
环境与能源
出版日期:
1986-09-30

文章信息/Info

Title:
The Stability and Local Truncation Error in Applying Gear’s Method to Second-Order Differential Equations
作者:
侯国屏
Author(s):
Hou Guoping
文献标志码:
A
摘要:
本文讨论了将Gear提出的数值积分方法直接用于微分方程组A d^2/〖dt〗^2 X+B d/dt X+CX=f时算法的稳定性与局部截断误差,证明了只要矩阵C非奇异,A、C均正定,B非负定时,一阶和二阶Gear法仍是绝对稳定的,其局部截断误差分别为0(h2)和0(h3)。
Abstract:
In this paper analysis is made of the stability and the local truncation error when the Gear’s Method is directly applied to the system of second order differential equations A d^2/〖dt〗^2 X+B d/dt X+CX=f.The conclusion obtained is that the first-order and second-order Gear methods still have the A-stability and their local truncation errors are respectively 0(h2) and 0(h3) provided matrix C is non-singular, A and C are positive definite, and B is non-negative definite.
更新日期/Last Update: 2016-05-23