Norm Form Of Quasi-linear Differential-algebraic Equations Near A Quasi-impasse Point

There is a wide range of applications for.differential algebraic equation models which in chemical engineering, mechanical, power system stability and many other fields of engineering Further analysis from theoretical and numerical aspects of differential algebraic equations have a good contribute to development of these related fields.In this paper, we focus on the singularity propertiess of quasilinear differential-algebraic equation. On the found of the analysis about the basic theory of differential-algebraic equations,In recent years people through reseach about semi-dominant differential algebraic equations of the content,we discussed the content of quasilinear differential--algebraic equation in a special class of singular points we have named quasi-barrier point, and by singular points of semi-dominant differential-algebraic equations is given the knowledge of quasilinear differential-algebraic equation to be obstacles to the definition of points, and discussed the basis of quasilinear differential-algebraic equation to be obstacles to the neighborhood near the standard form, namely, quasilinear differential-algebraic equations is given in such cases and the corresponding solutions of ordinary differential equations to be between. Through discussion of these forms more simple to be ordinary differential equations, we can be informed of the initial linear differential algebraic equations with natureSpecific ideas that first we use Gaussian elimination theory of linear differential-algebraic equations to be simplified, then also by matrix generalized inverse theory, to more complex linear differential-algebraic equations to be reduced to a semi-dominant form of differential algebraic equations. Then use the standard semi-explicit differential algebraic equations form the theoretical, by constructing a diffeomorphism transformation and the transformation of the diffeomorphism given under quasilinear differential-algebraic equation to be obstacles in the standard form near the form. So the normal forOm theory to application and development of further. And on this basis, we further discussed the application of such standard form in the problems encountered, and give treatment to be its desingularization, solve the difficulties encountered, given the more general standard simpler shaped form, there are two standards discussed in the shape of the differences and similarities between the solutions.