Petzold, Linda R. Recent developments in the numerical solution of differential/algebraic systems. (English) Zbl 0692.65037 Computational aspects of VLSI design with an emphasis on semiconductor device simulation, Proc. SIAM/AMS Summer Semin., Minnesota/MN (USA) 1987, Lect. Appl. Math. 25, 177-190 (1990). [For the entire collection see Zbl 0685.00023.] The paper surveys some recent developments in the numerical solution of nonlinear differential-algebraic systems \(F(t,y,y')=0\) where y is given initially and \(\partial F/\partial y'\) may be singular, looks at their classification by degree of singularity, gives convergence results for backward differentiation formulas, discusses the use of implicit Runge- Kutta methods and explores at methods for obtaining consistent initial conditions. Reviewer: J.D.P.Donnelly MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems Keywords:nonlinear differential-algebraic systems; convergence; backward differentiation formulas; implicit Runge-Kutta methods; consistent initial conditions Citations:Zbl 0685.00023 Software:DASSL PDFBibTeX XML