ODE methods for the solution of differential/algebraic systems. (English) Zbl 0557.65053

Gear, C. W.; Petzold, L. R.

SIAM J. Numer. Anal. 21, 716-728 (1984).

This paper deals with a number of theoretical results for the differential/algebraic equation \(F(t,y,y')=0\), where F,y,y’ are s- dimensional vectors. Many of these problems can be solved conveniently and economically using numerical ODE methods. Other problems cause serious difficulties for these methods. The authors’ purpose is first to examine those classes of problems that are solvable by ODE methods, and to indicate which methods are most advantageous for this purpose. Secondly, such problems are described which are not solvable by ODE methods. Finally, the authors give a reduction technique which allows systems to be reduced to ones that can be solved by numerical methods.

Reviewer: P.Chocholatý

MSC:

65L05	Numerical methods for initial value problems involving ordinary differential equations
65J99	Numerical analysis in abstract spaces

Keywords:

nilpotency; singularity; matrix pencils; differential/algebraic; equation; backward Euler method; Runge-Kutta methods; extrapolation methods

Software:

DASSL