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T. Sickenberger, E. Weinmüller, R. Winkler:
"Local error estimates for moderately smooth ODEs and DAEs";
in: "ASC Report 16/2007", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2007, ISBN: 978-3-902627-00-1.

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.

Local error estimation, Step-size control, Adaptive methods, Initial Value

http://www.asc.tuwien.ac.at/preprint/2007/asc16x2007.pdf