This is a manuscript of the paper
Lawrence F. Shampine, Mark W. Reichelt, and Jacek A. Kierzenka,
Solving Index-1 DAEs in MATLAB and Simulink,
SIAM Review, Vol. 18, No. 3, pp. 538-552, 1999.
The paper describes mathematical and software developments needed for effective solution of differential algebraic equations of index 1. Modifications introduced to ODE15S and ODE23T in MATLAB 5.3 allow for solving linearly-implicit DAEs of index 1.
The M-files for all the original examples described in the paper are available in the directory DAE_examples.
The directory DAE_examples_65 contains the files for the examples updated to take advantage of features available in MATLAB 6.5 (R13). Correspondingly, DAE_examples_70 contains files modified for use with MATLAB 7.0 (R14).
The paper describes solving linearly-implicit DAEs with time-dependent, singular mass matrix
M(t)*y' = f(t,y)
In MATLAB 6.0, the solvers were extended to handle DAEs with state-dependent mass matrices