Approximation of solutions to abstract neutral differential equations with non-instantaneous impulses

In this manuscript, we consider a class of first order abstract neutral differential equations with non-instantaneous impulses in an arbitrary separable Hilbert space and study the approximation of solutions. In order to define approximation, we use a projection scheme of increasing subspaces and projection operators. We establish the existence of approximate solutions and their convergence by using the Banach fixed point theorem and analytic semigroup theory. Also, we study the Faedo-Galerkin approximate solutions and their convergence to the solution of our given problem. At last, an example involving partial differential equation is presented for illustrating the discussed abstract results.