中文摘要：

本文讨论了一类具有较强应用背景的二维半线性伪抛物方程，设计了求解此类方程对应的初边值问题的隐式差分格式。基于离散泛函理论和先验估计证明了相应差分格式解的存在唯一性、收敛性和稳定性。最后针对实例给出了数值模拟结果。

英文摘要：

A type of 2D semi-linear pseudo-parabolic equation is considered, which has wide application areas. An implicit difference scheme corresponding to the IBVP of this equation is designed. By the discrete functional theory and prior estimate, the existence arid uniqueness of the solution to the nonlinear scheme, the convergence and the stability of the scheme are all proved. Some numerical results are finally presented for illustration.