Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations

In this paper, we propose a reliable algorithm to develop exact and approximate solutions for the linear and nonlinear Schrödinger equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.