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One-step and extrapolation methods for differential-algebraic systems. (English) Zbl 0635.65083
This paper analyzes one-step methods for differential-algebraic equations \(By'=f(y)\) \((y\in {\mathbb{R}}^ m\), \(B\in {\mathbb{R}}^{m\times m}\) is singular) with \(s=1\), where s is the index of nilpotency of the matrix pencil \([B-\lambda f_ y]\). An extrapolation algorithm based on semi- implicit Euler discretization is derived and its performance is compared with that of the codes of L. Petzold [A description of DASSL: a differential/algebraic system solver. Proc. IMACS World Congress 1982 (to appear)] and A. C. Hindmarsh [LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM-SIGNUM Newsletter 15, 10-11 (1980)]. The test examples are taken from chemical combustion.
Reviewer: V.A.Velev

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
80A25 Combustion
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