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Convergence of multistep time discretizations of nonlinear dissipative evolution equations

In English

Författare

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.

Avdelning/ar

Publiceringsår

2006

Språk

Engelska

Sidor

55-65

Publikation/Tidskrift/Serie

SIAM Journal on Numerical Analysis

Volym

44

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

Society for Industrial and Applied Mathematics

Ämne

  • Mathematics

Nyckelord

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

Status

Published

Forskningsgrupp

  • Partial differential equations
  • Numerical Analysis

ISBN/ISSN/Övrigt

  • ISSN: 0036-1429