Differential-Algebraic Equations (DAEs) in the form g(t,y,y')= 0, arise in many mathematical models. A class of Boundary Value Methods [3], namely the Generalized Backward Differentiation Formulas (GBDFs), seems to be suitable for the numerical solution of DAEs. In [4] the convergence properties of GBDFs for nonlinear semi-explicit index one DAEs are analyzed for initial and boundary value problems. The problem of computing consistent initial values is stated in [1,2] for nonlinear index 1, 2 and 3 DAEs of Hessenberg form, and an algorithm to compute consistent initial values for fully implicit nonlinear DAEs is also developed in [4]. In this talk we discuss the convergence properties of GBDFs and the computation of consistent initial values for more general classes of problems.

References

[1] P. Amodio, F. Mazzia, Numerical solution of differential algebraic equation and computation of consistent initial/boundary conditions, Journal of Computational and Applied Mathematics, 82 (1-2), 299-311 (1997).

[2] P. Amodio, F. Mazzia, An algorithm for the computation of consistent initial values for differential-algebraic equations, Numerical Algorithm 19 (1-4), 13-23 (1998).

[3] L. Brugnano, D. Trigiante, Solving Differential Problems by Multistep Initial and Boundary Value Methods, Gordon & Breach, Amsterdam, 1998.

[4] F. Mazzia, Boundary Value Methods for the numerical solution of Boundary Value Problems in Differential-Algebraic Equations, Bollettino U.M.I., 7 (11-A), 135-146 (1997).

MINISIMPOSIUM SESSION: 17. Software isues in ODEs