Deuflhard, P.; Hairer, E.; Zugck, J. One-step and extrapolation methods for differential-algebraic systems. (English) Zbl 0635.65083 Numer. Math. 51, 501-516 (1987). 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 Cited in 6 ReviewsCited in 57 Documents MSC: 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 80A25 Combustion Keywords:one-step methods; differential-algebraic equations; index of nilpotency; matrix pencil; extrapolation algorithm; semi-implicit Euler discretization; test examples; chemical combustion Software:DASSL × Cite Format Result Cite Review PDF Full Text: DOI EuDML References: [1] Bader, G., Deuflhard, P.: A Semi-Implicit Midpoint Rule for Stiff Systems of Ordinary Differential Equations. Numer. Math.41, 373-398 (1983) · Zbl 0522.65050 · doi:10.1007/BF01418331 [2] Deuflhard, P.: Recent Progress in Extrapolation Methods for Ordinary Differential Equations. SIAM Rev.27, 505-535 (1985) · Zbl 0602.65047 · doi:10.1137/1027140 [3] Deuflhard, P.: Order and Stepsize Control in Extrapolation Methods. Numer. 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