Abstract :
Singularly perturbed nonlinear differentialralgebraic equations DAE’s.are
considered, which are decomposed into two auxiliary problems, called the outer
and inner problems, respectively. The structure of solutions of the singularly
perturbed DAE’s is determined by the outer and inner solutions, both of which are
proved to exist. Asymptotic expansions for outer and inner solutions are obtained
and proved to be uniformly convergent. This generalizes known results about
asymptotic expansions of singularly perturbed ordinary differential equations.
The presentation of this work is separated into two parts because of the
limitation of space. The first part concerns the derivation of outer and inner
problem, and the existence and asymptotic expansion of outer solutions, while the
second part mainly focuses on the inner problem
