Local error estimates for moderately smooth problems: Part II-SDEs and SDAEs with small noise

Thorsten Sickenberger, Ewa Weinmüller, Renate Winkler

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index-1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we developed local error estimates for the case when the problem data is only moderately smooth, which is typically the case in stochastic differential equations. In this second part, we will consider the estimation of local errors in context of mean-square convergent methods for stochastic differential equations (SDEs) with small noise and index-1 stochastic differential-algebraic equations (SDAEs). Numerical experiments illustrate the performance of the mesh adaptation based on the local error estimation developed in this paper. © 2009 Springer Science + Business Media B.V.

Original languageEnglish
Pages (from-to)217-245
Number of pages29
JournalBIT Numerical Mathematics
Volume49
Issue number1
DOIs
Publication statusPublished - Mar 2009

Keywords

  • Adaptive methods
  • Local error estimation
  • Mean-square numerical methods
  • Small noise
  • Step-size control
  • Stochastic differential equations
  • Stochastic differential-algebraic equations

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