Local Error Estimates for Moderately Smooth ODEs and DAEs

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