Two Numerical Methods for Solving the Schrödinger Parabolic and Pseudoparabolic Partial Differential Equations

Source abstract

In this work, the initial-boundary value problems for one-dimensional linear time-dependent Schrödinger parabolic and pseudoparabolic partial differential equations are studied. The modified double Laplace decomposition method is applied to get the semianalytic solutions and the explicit finite difference method to get the approximate solutions of the problems. The von Neumann stability analysis of the presented problems is also investigated.