一类单部件可修系统解的半离散化

The semi-discretization of a repairable system with some singleness components

为解决一类单部件可修系统模型的数值计算问题,首先用半离散化方法对该系统模型中的修复率μ(x)进行离散,得到离散后的偏微分方程;然后用算子半群的知识将偏微分方程转化成矩阵常微分方程,根据Trotter逼近定理证明离散后方程的解逼近原方程的解。结果表明,将半离散化方法应用到该系统模型中是可行的,从而为其进一步的数值计算提供了理论基础。

To settle the problem of the calculation of the repairable system with some singleness components. By applying the semi-discretization method to disperseμ （x） in the model, the partial differential equation is obtained. Then the knowledge of arithmetic semi-group to transform is used to taransform the partial differential equation to a matrix ordinary differential. Finally, according to Trotter theory, it is shown that the solution the differential equation converges to the original equation, which states feasibility of applying the semi-discretization method to the con- sidered model and offers the foundation of theory to numerical computation.