Collocation Software for Boundary Value Differential-Algebraic Equations

We describe the methods and implementation of a general-purpose code, COLDAE. This code can solve boundary value problems for nonlinear systems of semi-explicit diierential-algebraic equations (DAEs) of index at most 2. Fully implicit index-1 boundary value DAE problems can be handled as well. The code COLDAE is an extension of the package COLNEW (COLSYS) for solving boundary value ODEs. The implemented method is piecewise polynomial collocation at Gaussian points, extended as needed by the projection method of Ascher-Petzold. For general semi-explicit index-2 problems, as well as for fully implicit index-1 problems, we deene a selective projected collocation method, and demonstrate its use. The mesh selection procedure of COLSYS is modiied for the case of index-2 constraints. We also discuss shooting for initial guesses. The power and generality of the code are demonstrated by examples.