中文摘要：

讨论了一类半线性抛物型微分包含第一边值问题的有限维逼近，研究了其近似可解性．在本文定义的网格范数意义下，空间方向的有限差分半离散化差分解收敛到问题的解，同时也证明了全离散差分格式对初值是稳定的．最后通过一个具体的一维半线性抛物刑微分包含实例，对本文的差分格式进行了验证．

英文摘要：

The discrete approximations for a class of semilinear parabolic differential inclusions is discussed. By the definition of the mesh norm, the finite difference discrete scheme of spacial convergences to the solution. The finite difference discrete scheme is stability for the initial value. An example to illustrate the numerical implementation is also presented.