Results on approximate solutions of second order differential equations with non-instantaneous impulses in a separable Hilbert space

This paper is concerned with the approximation of solutions to a class of second order non linear non-instantaneous impulsive abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operators. We investigate the connection between the approximate solutions 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, some examples of abstract formulation are provided.