UM ETheses Collection (澳門大學電子學位論文庫)
 Title

A linearized CCD method for timefractional and integer order Schrodinger equations
 English Abstract

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In this thesis, we consider the numerical solutions of two different kinds of Schr¨odinger equations, named timefractional 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 L1CCD method for solving the timefractional 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 CCDPRADI method [21], we develop a linearized CCDPRADI method for solving the 2D cubic nonlinear Schr¨odinger equation. The linearized CCDPRADI method is also unconditionally stable. Numerical experiments are conducted to test the high order accuracy of the linearized CCDPRADI 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
 Location
 1/F Zone C
 Library URL
 991000748799706306