Desingularizing Of Differential-Algebraic Equations

Differential algebraic equations in linear (or nonlinear) circuits, power systems, chemical engineering, electrical engineering and other fields have a wide range of applications. In these applications, mostly for the autonomous system The differential-algebraic equations. the research on the DAEs, the singularity analysis of an important position, it is also the singular DAEs allows differential algebraic equations with the unique nature different from the ODE. It can be seen, singular point is to make the differential-algebraic equations The reason is different from the critical point differential. R.RIAZA use of ideas discussed to singular differential algebraic equations in the non-degenerate singular point singular point near the crossover phenomenon. Reference the ideas of R. RIAZA, methods of this paper is to discuss the singularity of the form of the DAEs system near the singular manifold properties of solutions. The nature of this method is in the singularity neighborhood of the system re-scaling the DAEs into equivalence of differential equations to study. This will result Marszaler singular manifold extended to the case, given the DAEs in the non-degenerate singular point near the geometric singularity of smooth solutions, however, two sufficient conditions for the existence and convergence.This paper is divided into four parts mainly.The first part introduces the differential-algebra equations'the historical background, the dynamic and development trend.The second part introduces the concept of singularity of differential-algebraic equations.The third part gives a demonstration of the geometry singularity to the three cases by strange ideas, analyses the nature of its smooth the possibility.The fourth section was further proved by the singularity and smooth the two full term in nature and convergence.