Local error control for general index-1 and index-2 differential-algebraic equations

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.