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BIT Numerical Mathematics

, Volume 47, Issue 1, pp 157–187 | Cite as

Local error estimates for moderately smooth problems: Part I – ODEs and DAEs

  • Thorsten Sickenberger
  • Ewa Weinmüller
  • Renate Winkler
Article

Abstract

The paper consists of two parts. In the first part, we propose 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 develop local error estimates for the case when the problem data is only moderately smooth. Numerical experiments illustrate the performance of the mesh adaptation based on the error estimation developed in this paper. In the second part of the paper, we will consider the estimation of local errors in context of stochastic differential equations with small noise.

Key words

local error estimation step-size control adaptive methods initial value problems differential-algebraic equations defect correction 

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Copyright information

© Springer Science + Business Media B.V. 2006

Authors and Affiliations

  • Thorsten Sickenberger
    • 1
  • Ewa Weinmüller
    • 2
  • Renate Winkler
    • 1
  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Institut für Analysis und Scientific ComputingTechnische Universität WienWienAustria

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