school

UM E-Theses Collection (澳門大學電子學位論文庫)

check Full Text
Title

A linearized CCD method for time-fractional and integer order Schrodinger equations

English Abstract

In this thesis, we consider the numerical solutions of two different kinds of Schr¨odinger equations, named time-fractional nonlinear Schr¨odinger equation and integer order cubic nonlinear Schr¨odinger equation respectively. An introduction is first given in Chapter 1. In Chapter 2, we propose a linearized L1-CCD method for solving the time-fractional nonlinear Schr¨odinger equation. The unconditional stability is verified by mean of linear Fourier analysis. Numerical examples are conducted to show the high order accuracy of the proposed scheme. In Chapter 3, to improve the efficiency of the iterative CCD-PRADI method [21], we develop a linearized CCD-PRADI method for solving the 2D cubic nonlinear Schr¨odinger equation. The linearized CCD-PRADI method is also unconditionally stable. Numerical experiments are conducted to test the high order accuracy of the linearized CCD-PRADI method and to illustrate the drifting solution pattern of the nonlinear Schr¨odinger equation.

Issue date

2015

Author

Jin, Jun Wei

Faculty

Faculty of Science and Technology

Degree

M.Sc.

Subject

Schrödinger equation

Mathematics -- Department of Mathematics

Supervisor

Sun, Hai Wei

Files In This Item

Full-text (internet)

Location
1/F Zone C
Library URL
991000748799706306