两相同部件温贮备可修人机系统解的半离散化

The semi-discretization of repairable,warm standby,man-machine system with two identical units

为解决利用数值研究两相同部件温贮备可修人机系统的计算问题,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,将半离散算法应用到两相同部件温贮备可修人机系统模型中,对系统中的修复率u(x)进行离散,得到该系统的半离散化模型;运用泛函分析理论证明该算法的收敛性。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 computing problem when the repairable, warm standby, man-machine system with two identical units is studied through numerical methods. The semi-discretization approximation method is employed to transform a parabolic partial differential equation into a matrix ordinary differential equation, and the semi-discretization algorithm is applied to the model of the repairable, warm standby, man-machine system with two identical units. The repair rate u（x） in the system is discretized to obtain a semi-discretization model of the system. The theory of functional analysis is used to prove the conver- gence of the semi-discretization algorithm. In conclusion, the solution of the discretized equation conver- ges to the solution of the original equation, which provides a theoretical foundation for further research on numerical calculation.