Optimal error estimates for high order runge-kutta methods applied to evolutinary equations

Author

William R. McKinney

Date of Award

8-1989

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Ohannes Karakashian

Committee Members

Nicholas D. Alikakos, Steven M. Serbin, Don Hiinton, George Condo

Abstract

Fully discrete approximations to 1-periodic solutions of the Generalized Korteweg de-Vries and the Cahn-Hilliard equations are analyzed. These approximations are generated by an Implicit Runge-Kutta method for the temporal discretization and a Galerkin Finite Element method for the spatial discretization. Furthermore, these approximations may be of arbitrarily high order. In particular, it is shown that the well-known order reduction phenomenon afflicting Implicit RungeKutta methods does not occur. Numerical results supporting these optimal error estimates for the Korteweg-de Vries equation and indicating the existence of a slow motion manifold for the Cahn-Hilliard equation are also provided.

Recommended Citation

McKinney, William R., "Optimal error estimates for high order runge-kutta methods applied to evolutinary equations. " PhD diss., University of Tennessee, 1989.
https://trace.tennessee.edu/utk_graddiss/11721