A conservative numerical method for a class of unstable nonlinear Schrödinger equation

Author

Wang, Zhen ; Huang, Xia

Author_Institution

Sch. of Autom., Nanjing Univ. of Sci. & Technol., Nanjing, China

Volume

9

fYear

2010

fDate

22-24 Oct. 2010

Abstract

This paper is concerned with the numerical solution to a class of unstable nonlinear Schrödinger equations. A conservative numerical scheme is devised, and three of its discrete conservation laws are proved. Meanwhile, stability and convergence of such scheme with second order convergence rate of time and space are proved by the energy method. In addition, a numerical example is given to demonstrate the accuracy and efficiency of the proposed method.

Keywords

Schrodinger equation; finite difference methods; nonlinear differential equations; numerical stability; conservative numerical method; conservative numerical scheme; discrete conservation laws; energy method; finite difference method; numerical solution; scheme convergence; scheme stability; unstable nonlinear Schrodinger equation; Computer applications; Convergence; Equations; Mathematical model; Modeling; Solitons; Stability analysis; UNLS equation; conservative law; convergence; finite difference method;

fLanguage

English

Publisher

ieee

Conference_Titel

Computer Application and System Modeling (ICCASM), 2010 International Conference on

Conference_Location

Taiyuan

Print_ISBN

978-1-4244-7235-2

Electronic_ISBN

978-1-4244-7237-6

Type

conf

DOI

10.1109/ICCASM.2010.5623051

Filename

5623051