Singularly Perturbed DifferentialrAlgebraic Equations. I: Asymptotic Expansion of Outer Solutions

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