error estimate linear multi-step method local truncation error iterated defect correction step-size control ODE DAE Local error estimates for moderately smooth ODEs and DAEs Thorsten Sickenberger Sickenberger Thorsten Ewa Weinmüller Weinmüller Ewa Renate Winkler Winkler Renate Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27 pages

Local error estimates for moderately smooth ODEs and DAEs

Thorsten Sickenberger , Ewa Weinmüller , Renate Winkler

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 27 pages

MSC 2000

65L06 Multistep, Runge-Kutta and extrapolation methods
65L80 Methods for differential-algebraic equations

Abstract
We discuss an error estimation procedure for the local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index 1 differential-algebraic equations (DAEs). The proposed error estimation strategy is based on the principle of Defect Correction. Here, we present how this idea can be adapted for the estimation of local errors in case when the problem data is only moderately smooth. Moreover, we illustrate the performance of the mesh adaptation based on the error estimation developed in this paper.

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