A Proposed Numerical Algorithm for Solving Nonlinear Index Problems

In this paper, we present and demonstrate a numerical algorithm to detect and solve mixed systems of nonlinear ordinary differential and algebraic equations that have an index problem. Symbolic differentiation is used to generate the equations needed; symbolic elimination is not required as in many other algorithms. We show that the so-called initialization and propagation problems are in fact the same problem; they can therefore be handled by a common approach. Numerical as well as structural singularities arising in index problems are accommodated. In principle, the algorithm can be used with any integration scheme, including an explicit one. This algorithm is suitable for solving index problems that previously could not be solved.