In this paper, a perturbing nonlinear Schrodinger equation is studied under limited time interval through homogeneous
boundary conditions and real initial condition. The analytical solution for the linear case is introduced. The perturbation
method is used to introduce an approximate solution for the perturbative nonlinear case for which a power series
solution is proved to exist. Using Mathematica, the solution algorithm is tested through first order approximation. The
method of solution is illustrated through case studies and figures.