Runge-Kutta time discretizations of nonlinear dissipative evolution equations
(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:
https://lup.lub.lu.se/record/413980
- author
- Hansen, Eskil LU
- organization
- publishing date
- 2006
- 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
- 2024-07-16 13:56:02
@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}}, keywords = {{B-convergence; Runge-Kutta methods; m-dissipative maps; nonlinear evolution equations; logarithmic Lipschitz constants; algebraic stability}}, 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}}, }