Numerical simulation of singular solutions of the Generalized Korteweg - de Vries Equation

Author

Janusz Kolodziejczyk

Date of Award

8-1998

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Ohannes Karakashian

Committee Members

Steven Serbin, Xiaobing Feng, Grzegorz Kawiecki

Abstract

A fully discrete approximation to the solution of the Generalized Korteweg - de Vries Equation is presented and analyzed. The presented numerical method is aimed at approximating solutions developing blow-up singularities. The spatial discretization is based on polynomial spline, adaptive finite elements and the temporal discretization is achieved by a variable step Crank-Nicolson scheme. The numerical scheme employs a spatial refinement strategy which allows the mesh to be refined locally and without compromising the overall quality of the mesh. Several numerical experiments concerning the formation of singularities are presented.

Recommended Citation

Kolodziejczyk, Janusz, "Numerical simulation of singular solutions of the Generalized Korteweg - de Vries Equation. " PhD diss., University of Tennessee, 1998.
https://trace.tennessee.edu/utk_graddiss/9288