Jan Sieber
Local error control for general index-1 and index-2 differential algebraic equations
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

65L50 Mesh generation and refinement

65L05 Initial value problems

65L06 Multistep, Runge-Kutta and extrapolation methods

65L08 Improperly posed problems

Abstract: This paper presents an error test function usable for the local error control and the automatic stepsize selection in the numerical integration of general index-1 and index-2 differential-algebraic equations (DAEs). This test function makes a compromise between a good approximation of the error arising per step by the discretization (local error) and the order and smoothness assumptions made by the stepsize selection schemes, that are widely used in present codes. Its computation is of moderate costs and does not require additional information about the structure of the DAE from outside.
Keywords: differential algebraic equations, numerical integration, error control, stepwise selection, local error control