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Runge-Kutta time discretizations of nonlinear dissipative evolution equations

Hansen, Eskil LU (2006) In Mathematics of Computation 75(254). p.631-640
Abstract
Global error bounds are derived for Runge-Kutta time discretizations of fully nonlinear evolution equations governed by m-dissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants in order to extend the classical B-convergence theory to infinite-dimensional spaces. An algebraically stable Runge-Kutta method with stage order q is derived to have a global error which is at least of order q - 1 or q, depending on the monotonicity properties of the method.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
B-convergence, Runge-Kutta methods, m-dissipative maps, nonlinear evolution equations, logarithmic Lipschitz constants, algebraic stability
in
Mathematics of Computation
volume
75
issue
254
pages
631 - 640
publisher
American Mathematical Society (AMS)
external identifiers
  • wos:000236723300005
  • scopus:33646422486
ISSN
1088-6842
DOI
10.1090/S0025-5718-05-01866-1
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
e5ecae22-a6a9-41c7-a92e-792b8a1cdabe (old id 413980)
date added to LUP
2016-04-01 12:08:27
date last changed
2020-12-29 01:52:59
@article{e5ecae22-a6a9-41c7-a92e-792b8a1cdabe,
  abstract     = {Global error bounds are derived for Runge-Kutta time discretizations of fully nonlinear evolution equations governed by m-dissipative vector fields on Hilbert spaces. In contrast to earlier studies, the analysis presented here is not based on linearization procedures, but on the fully nonlinear framework of logarithmic Lipschitz constants in order to extend the classical B-convergence theory to infinite-dimensional spaces. An algebraically stable Runge-Kutta method with stage order q is derived to have a global error which is at least of order q - 1 or q, depending on the monotonicity properties of the method.},
  author       = {Hansen, Eskil},
  issn         = {1088-6842},
  language     = {eng},
  number       = {254},
  pages        = {631--640},
  publisher    = {American Mathematical Society (AMS)},
  series       = {Mathematics of Computation},
  title        = {Runge-Kutta time discretizations of nonlinear dissipative evolution equations},
  url          = {http://dx.doi.org/10.1090/S0025-5718-05-01866-1},
  doi          = {10.1090/S0025-5718-05-01866-1},
  volume       = {75},
  year         = {2006},
}