具有软硬件可修复计算机系统解的半离散化  

Semi-discretization of repairable computer system with hardware and software

作　　者：周莉[1] 张敬[1] 魏新[1] 

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《辽宁工程技术大学学报（自然科学版）》2012年第2期276-279,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：黑龙江省教育厅科学技术研究基金资助项目(12511609)

摘　　要：为了解决利用数值计算研究具有软硬件可修复计算机串联系统模型的问题,利用半离散化逼近方法将一个抛物型偏微分方程化为矩阵常微分方程,且后者在许多问题上可以作为原问题的近似.将半离散算法应用到具有软硬件可修复计算机系统模型中,对系统中的修复率进行离散,得到了该系统的半离散化模型,运用泛函分析理论证明了半离散算法的收敛性,结果表明:离散后方程的解收敛于原方程的解,从而为该模型进一步的数值计算提供了理论基础.To solve the problem with the model of series repairable computer system with hardware and software,this study uses semi-discretization approximation method to transform a parabolic partial differential equation into a matrix ordinary differential equation,which can be regarded as similar solution of the original problem.Therefore,this study applies a semi-discretization algorithm to the model of series repairable computer system with hardware and software,and discretizes the model to obtain a semi-discretization model.Subsequently,the theory of functional analysis is used to prove the convergence of the semi-discretization algorithm.The discretized equation converges to the original equation.This study provides a theoretical foundation for farther research on numerical calculation.

关 键 词：可修复系统 串联 半离散化 逼近 C0半群 算子 收敛 积分微分方程 

分 类 号：O175.6[理学—数学]