Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations
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 Runge Kutta 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.
- Authors:
- Publication Date:
- Research Org.:
- Tennessee Univ., Knoxville, TN (United States)
- OSTI Identifier:
- 5241289
- Resource Type:
- Miscellaneous
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; KORTEWEG-DE VRIES EQUATION; RUNGE-KUTTA METHOD; ERRORS; GALERKIN-PETROV METHOD; MATHEMATICAL MANIFOLDS; PROBABILISTIC ESTIMATION; DIFFERENTIAL EQUATIONS; EQUATIONS; ITERATIVE METHODS; NUMERICAL SOLUTION; PARTIAL DIFFERENTIAL EQUATIONS; 990200* - Mathematics & Computers
Citation Formats
McKinney, W R. Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations. United States: N. p., 1989.
Web.
McKinney, W R. Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations. United States.
McKinney, W R. 1989.
"Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations". United States.
@article{osti_5241289,
title = {Optimal error estimates for high order Runge-Kutta methods applied to evolutionary equations},
author = {McKinney, W R},
abstractNote = {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 Runge Kutta 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.},
doi = {},
url = {https://www.osti.gov/biblio/5241289},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 1989},
month = {Sun Jan 01 00:00:00 EST 1989}
}
Other availability
Please see Document Availability for additional information on obtaining the full-text document. Library patrons may search WorldCat to identify libraries that may hold this item.
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.