This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided.

翻译：本文研究一类二阶非线性抽象微分方程解的逼近问题。借助投影算子构造给定系统的有限维近似解，探讨近似解与精确解之间的关系及收敛性问题。进一步定义Faedo-Galerkin(F-G)逼近，证明其存在性与收敛性结果。利用余弦函数理论、Banach不动点定理及闭线性算子的分数次幂等工具获得相关结论。最后给出一个抽象形式的算例。