Based on the generalized bottom boundary condition proposed by Cheng, Cheng derived an analytical solution with compli-cated form and we need to solve two transcend equations in order to get the analytical solution. In this paper, we analyse the difficulties in the analytical solution calculation.We reduce the searching regions for finding roots of the transcend equations easily. On the other hand, according to the numerical results,we found that the constructed difference schemes with scheme parameter 0.48≤Θ≤1 are stable and identify with the analytical solution.