A fast method to implement non-local discrete transparent boundary conditions for the Schrödinger equation

Discrete transparent boundary conditions for the two dimensional Schrödinger equation

This paper is concerned with transparent boundary conditions (TBCs) for the time–dependent Schrödinger equation on a circular domain. Discrete TBCs are introduced in the numerical simulations of problems on unbounded domains in order to reduce the computational domain to a finite region in order to make this problem feasible for numerical simulations. The main focus of this article is on the ap...

Discrete Transparent Boundary Conditions for the Schrödinger Equation

This paper is concerned with transparent boundary conditions for the one dimensional time–dependent Schrödinger equation. They are used to restrict the original PDE problem that is posed on an unbounded domain onto a finite interval in order to make this problem feasible for numerical simulations. The main focus of this article is on the appropriate discretization of such transparent boundary c...

Absorbing Boundary Conditions for the Schrödinger Equation

A large number of differential equation problems which admit traveling waves are usually defined on very large or infinite domains. To numerically solve these problems on smaller subdomains of the original domain, artificial boundary conditions must be defined for these subdomains. One type of artificial boundary condition which can minimize the size of such subdomains is the absorbing boundary...

Splitting in Potential Finite-Difference Schemes with Discrete Transparent Boundary Conditions for the Time-Dependent Schrödinger Equation

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...