Superstiffness Phenomenon and Solution of the Differential-Algebraic Equations
by
Vladimir B. Mikhailov
CAD Institute of Russian Academy of Sciences

The differential-algebraic equations (DAE) arise in various areas of practical applications: electric circuits simulation; tensile strength dynamic systems, solid-state systems, simulation of physical and chemical processes, etc.

By DAE systems we assume the ordinary differential equations which cannot be solved concerning arguments. They may consist of the differential equations which are coupled with the algebraic finite-dimensional equations. As well, for DAE here singular systems, descriptive systems, and heterogeneous differential equations are meant.

One of the most intensively developing and effective directions of such systems solution are the numerical-analytical methods. The main problem in DAE solution is the reliability of the obtained results and its connection with increase of the system index.

The algorithms developed at present mainly deal with DAE of index 1 or 2. In the report some important results are presented which concern finding fast and exact numerical-analytical solutions of linear and nonlinear DAE of an arbitrary index with an arbitrary spectrum. They are obtained on the basis of effective for calculations analytical solution.

Also, the influence of a superstiffness phenomenon on reliability of numerical and numerical-analytical methods was investigated, as well as the problems of obtaining the analytical solutions on complex effecting functions, and approximating of nonlinear functionals, received at solution of DAE, were researched.

Date received: January 14, 2000