Behavior of the nonunique terms in general DAE integrators
The article is concerned with systems of differential-algebraic equations (DAEs), and their numerical solution. In general, numerical DAE solvers require to solve a system of nonlinear equations in each time step, the dimension of which depends on the index of the DAE and is larger than the dimension of the original DAE system. A part of the solution of the nonlinear system is usually not uniquely determined. It is shown that this part solves an auxiliary DAE which also depends on the predictor used in the Gauss-Newton iteration solving the system. As a consequence, criteria for the design of low-order integrators are established; in particular, explicit integration and implicit coordinate partitioning schemes of order lower than the index of the DAE, are justified.
systems of differential-algebraic equations
scientific article; zbMATH DE number 1311262