Runge-Kutta time discretizations of nonlinear dissipative evolution equations
Författare
Summary, in English
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.
Avdelning/ar
- Matematik LTH
- Partial differential equations
- Numerical Analysis
Publiceringsår
2006
Språk
Engelska
Sidor
631-640
Publikation/Tidskrift/Serie
Mathematics of Computation
Volym
75
Issue
254
Dokumenttyp
Artikel i tidskrift
Förlag
American Mathematical Society (AMS)
Ämne
- Mathematics
Nyckelord
- B-convergence
- Runge-Kutta methods
- m-dissipative maps
- nonlinear evolution equations
- logarithmic Lipschitz constants
- algebraic stability
Status
Published
Forskningsgrupp
- Partial differential equations
- Numerical Analysis
ISBN/ISSN/Övrigt
- ISSN: 1088-6842