Galerkin/Runge-Kutta discretization for the nonlinear Schrödinger equation

Author

Hyun Young Lee

Date of Award

12-1991

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Ohanes A. Karakashian

Committee Members

S. Jordan, S. Serbin, L. Tsoukalas

Abstract

A class of fully discrete high order Galerkin Runge-Kutta methods are constructed and analyzed for the nonlinear Schrodinger equation. Optimal order error estimates are established for the 0-boundary and periodic boundary value problems, and several computational results such as the order of the temporal accuracy, preservation of two invariants, various kinds of errors are presented. Furthermore, it is noted that these methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Recommended Citation

Lee, Hyun Young, "Galerkin/Runge-Kutta discretization for the nonlinear Schrödinger equation. " PhD diss., University of Tennessee, 1991.
https://trace.tennessee.edu/utk_graddiss/11159