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Runge-Kutta time discretizations of nonlinear dissipative evolution equations
Author(s):
Eskil
Hansen.
Journal:
Math. Comp.
75
(2006),
631-640.
MSC (2000):
Primary 65J15, 65M12
Posted:
December 19, 2005
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Abstract:
Global error bounds are derived for Runge-Kutta time discretizations of fully nonlinear evolution equations governed by  -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  -convergence theory to infinite-dimensional spaces. An algebraically stable Runge-Kutta method with stage order  is derived to have a global error which is at least of order  or  , depending on the monotonicity properties of the method.
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Additional Information:
Eskil
Hansen
Affiliation:
Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden
Email:
eskil@maths.lth.se
DOI:
10.1090/S0025-5718-05-01866-1
PII:
S 0025-5718(05)01866-1
Keywords:
Nonlinear evolution equations,
logarithmic Lipschitz constants,
$m$-dissipative maps,
Runge-Kutta methods,
algebraic stability,
$B$-convergence
Received by editor(s):
December 14, 2004
Posted:
December 19, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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