Authorized Name

Thick, Kyle

Abstract

Fractional partial differential equations (PDEs) have found success in recent decades in modeling several different phenomena in science and engineering. Analytic solutions for fractional PDEs are rare, so numerical approximations are often used instead. In the literature, few numerical methods for solving fractional PDEs with Riesz space fractional derivatives have been proposed. In particular, we are aware of no energy conserving method for solving the fractional nonlinear Schrodinger equation. We remedy this situation by modifing two methods found in the literature so that they are energy conserving. The first method which we call the Crank-Nicolson L2 method is proven to conserve both mass and energy. It is also shown to converge to the analytic solution with convergence rate O(h+T2). The second scheme, the Crank-Nicolson centered difference method, is also proven to conserve mass and energy. However, this method is proven to converge faster in space than the L2 method. The convergence rate for the method is shown to be O(h2+T2). Numerical results are provided to confirm what is proven analytically.

Advisor(s)

Zhang, Yanzhi

Department(s)

Mathematics and Statistics

Publisher

Missouri University of Science and Technology

Pagination

vi, 34 pages

Note about bibliography

Includes bibliographical references (pages 35-37)

Rights

© 2014 Kyle Thicke, All rights reserved

Document Type

Honors Thesis

File Type

text

Language(s)

English

Institutions Name at Time of Publication

Missouri University of Science and Technology

Download

Share

COinS