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Runge-Kutta time discretizations of nonlinear dissipative evolution equations

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Author

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.

Department/s

Publishing year

2006

Language

English

Pages

631-640

Publication/Series

Mathematics of Computation

Volume

75

Issue

254

Document type

Journal article

Publisher

American Mathematical Society (AMS)

Topic

  • Mathematics

Keywords

  • B-convergence
  • Runge-Kutta methods
  • m-dissipative maps
  • nonlinear evolution equations
  • logarithmic Lipschitz constants
  • algebraic stability

Status

Published

Research group

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 1088-6842