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Fariba Takhtabnoos, Ahmad Shirzadi * ; Persian Gulf University, Iran Received: 2 Jan 2018 Accepted: 19 Feb. 2018 Extended Abstract Paper pages (153-172) Introduction The time dependent Schrödinger equation with arbitrary potential function is a fundamental equation of quantum mechanics. It is well known that Schrödinger equation play an essential role in the relativistic and non-relativistic quantum mechanics. This equation arises in many other practical domains of physical and technological interest, e.g. optics, seismology and plasma physics. Many problems of solid state physics, atomic and molecular structure and spectra, molecular dynamics and quantum chemistry require the solution of the nonlinear time dependent Schrödinger equation. The nonlinear Schrödinger equation is a Generic model for the slowly varying envelop of a wave-train in conservative, dispersive, mildly nonlinear wave phenomena. It is also obtained as the subsonic limit of the Zakharov model for Langmuir waves in plasma physics. In more cases, the analytical solutions of these equations do not exist or finding their analytic solution is very difficult. Thus, presenting an accurate numerical method is an essential requirement in numerical analysis. In recent years, many papers have been published in the field of meshless methods. From a point of view they can be classified in two groups: one using a global strategy and another using local strategy. Meshless local Petrov-Galerkin and meshless local integral equation methods can be regarded as the oldest local treatments in the Meshless methods, where both testing and trial approximation are done locally. The Finite collocation (FC) method is another meshless local strategy for which, besides collocation of unknown solution in local subdomains, the PDE governing operator is also enforced in the local collocation systems. Based on the FC approach, this paper proposes a meshless local strategy for the numerical solution of nonlinear time dependent Schrödinger equation.

A Local Strong form Meshless Method for Solving 2D time-Dependent Schrödinger Equations