The browser you are using is not supported by this website. All versions of Internet Explorer are no longer supported, either by us or Microsoft (read more here: https://www.microsoft.com/en-us/microsoft-365/windows/end-of-ie-support).

Please use a modern browser to fully experience our website, such as the newest versions of Edge, Chrome, Firefox or Safari etc.

Convergence of multistep time discretizations of nonlinear dissipative evolution equations

På svenska

Author

Summary, in English

Global error bounds are derived for multistep time discretizations of fully nonlinear evolution equations on infinite dimensional 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 and nonlinear semigroups. The error bounds reveal how the contractive or dissipative behavior of the vector field, governing the evolution, and the properties of the multistep method influence the convergence. A multistep method which is consistent of order p is proven to be convergent of the same order when the vector field is contractive or strictly dissipative, i.e., of the same order as in the ODE-setting. In the contractive context it is sufficient to require strong zero-stability of the method, whereas strong A-stability is sufficient in the dissipative case.

Department/s

Publishing year

2006

Language

English

Pages

55-65

Publication/Series

SIAM Journal on Numerical Analysis

Volume

44

Issue

1

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Keywords

  • convergence
  • stability
  • multistep methods
  • dissipative maps
  • nonlinear evolution equations
  • logarithmic Lipschitz constants

Status

Published

Research group

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0036-1429