Runge-Kutta time discretizations of nonlinear dissipative evolution equations

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)631-640
TidskriftMathematics of Computation
Volym75
Nummer254
DOI
StatusPublished - 2006

Bibliografisk information

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004)

Ämnesklassifikation (UKÄ)

  • Matematik

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