An approximation for nonlinear differential-algebraic equations via singular perturbation theory

In this paper, we study jumps of nonlinear DAEs caused by inconsistent initial values. First, propose a simple normal form called the index-1 Weierstrass (INWF) for DAEs. Then generalize notion consistency projector linear to case. By an example, compare our proposed projectors with two existing consistent initialization methods show that are not coordinate-free, i.e., points calculated invariant under coordinates transformations. Next singular perturbed system approximation DAEs, which is ordinary differential equation (ODE) small perturbation parameter, solutions approximate both resulting from and $\mathcal C^1$-solutions DAE. At last, use numerical simulation DAE model arising electric circuit illustrate effectiveness