Finite-difference solutions of a non-linear Schrödinger

Authors:
F. Hosseini;V. Pouyafar;S. A. Sadough
Affiliations:
Center of Excellence in Solid Mechanics, Mechanical Engineering Department, AmirKabir University of Technology, Tehran Polytechnic, Tehran, Iran;Center of Excellence in Solid Mechanics, Mechanical Engineering Department, AmirKabir University of Technology, Tehran Polytechnic, Tehran, Iran;Center of Excellence in Solid Mechanics, Mechanical Engineering Department, AmirKabir University of Technology, Tehran Polytechnic, Tehran, Iran
Venue:
MACMESE'09 Proceedings of the 11th WSEAS international conference on Mathematical and computational methods in science and engineering
Year:
2009

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Abstract

The NLS equation has been shown to model a wide class of physical phenomena such as propagation of optical pulses, waves in water, waves in plasmas and self-focusing in laser pulses. Theoretical solution of this equation is unknown for the more general initial conditions. So, many studies have been dealt with getting the numerical solution of the NLS equation. The B-spline finite element methods has already been used to construct efficient and accurate solutions to some nonlinear and Schrödinger equation as well. In this paper a finite difference method is derived to solve one type of non linear Schrödinger and in order to solve the equation with derived formula and comparison with the result of B-spline method, numerical solution is used by Visual Fortran software. The output result is in good agreement with B-spline method which could be indicated the efficiency of this finite difference method for solution of non linear Schrödinger equation.