Transformation of Differential Algebraic Array Equations to Index One Form

Several new algorithms are proposed that in effect transform DAEs (Differential Algebraic Equations) to a special index one form that can be simulated with standard DAE integrators. The transformation to this form is performed without solving linear and/or nonlinear equation systems, the sparsity of the equations is kept, and array equations remain array equations or differentiated versions of them. Furthermore, certain DAEs can be handled where structural index reduction methods fail. It is expected that these new algorithms will help to treat large Modelica models of any index in a better way as it is currently possible. The algorithms have been evaluated and tested in the experimental simulation environment Modia that is implemented with the Julia programming language.