A flexible symplectic scheme for two-dimensional Schrödinger equation with highly accurate RBFS quasi-interpolation

Construction Techniques for Highly Accurate Quasi-Interpolation Operators

Under mild additional assumptions this paper constructs quasi -interpolants in the form f h (x) = +1 X j= 1 f(hj)' h x h j ; x 2 IR; h > 0 (0.1) with approximation order ` 1, where ' h (x) is a linear combination of translates (x jh) of a function in C ` (IR). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the function . This a...

Using multiquadric quasi-interpolation for solving Kawahara equation

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation

Using the three-order symplectic integrators and fourth-order collocated spatial differences, a highorder symplectic finite-difference time-domain (SFDTD) scheme is proposed to solve the time-dependent Schrödinger equation. First, the high-order symplectic framework for discretizing a Schrödinger equation is described. Then the numerical stability and dispersion analyses are provided for the FD...

Domain Decomposition Algorithms for Two Dimensional Linear Schrödinger Equation

This paper deals with two domain decomposition methods for two dimensional linear Schrödinger equation, the Schwarz waveform relaxation method and the domain decomposition in space method. After presenting the classical algorithms, we propose a new algorithm for the Schrödinger equation with constant potential and a preconditioned algorithm for the general Schrödinger equation. These algorithms...