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Numerical solution of nonlinear differential equations with algebraic constraints. II: Practical implications. (English) Zbl 0632.65086
In part I [Math. Comput. 46, 491-516 (1986; Zbl 0601.65060)] the authors showed that for systems of differential equations coupled with algebraic constraints the k-step constant stepsize backward differential formulas (BDF) method converges to order of accuracy \(O(h^ k)\), where h is the stepsize. In the present paper they investigate some of the practical difficulties of implementing variable step-size BDF, showing how to overcome problems of ill-conditioned matrices, and giving convergence tests which are supported by theory.
Reviewer: L.M.Berkovich

MSC:
65L05 Numerical methods for initial value problems
65L20 Stability and convergence of numerical methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
Software:
DASSL
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