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Index-2 differential-algebraic equations. (English) Zbl 0667.34014

A class of general nontransferable differential-algebraic equations which contains all linear differential-algebraic equations having the global index 2 in the definition of Gear and Petzold or being tractable with index 2 in the sense of Griepentrog and März as well as nonlinear index-2 equations in the understanding of Brenan, Gear, Petzold and further authors is characterized by a uniform matrix criterion. Existence and uniqueness statements are proved.

MSC:

34A30 Linear ordinary differential equations and systems
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[1] Gantmakher, F. R.: Teoriya matrits. Moskva: Nauka, 1966
[2] Griepentrog, E.; März, R.: Differential-algebraic equations and their numerical treatment. Leipzig: BSB B. G. Teubner Verlagsgesellschaft, 1986 (Teubner-Texte zur Mathem., 88) · Zbl 0629.65080
[3] Gear, C. W.; Petzold, L. R.: Differential/algebraic systems and matrix pencils. - In: Matrix Pencils/ eds. Kågström, B.; Ruhe, A.- Berlin: Springer, 1983, 75–89 (Lecture Notes in Math., 973) · Zbl 0494.65038
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[8] März, R.: On the numerical treatment of differential-algebraic equations. -To appear in ZAMM
[9] Brenan, K. E.; Enquist, B. E.: Backward difference approximations of nonlinear differential-algebraic equations.- California, El Segundo, The Aerospace Corporation, 1985 (Aerospace Report, ATR-85(9990)-5)
[10] Lötstedt, P.; Petzold, L.: Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas. -Math. Comp. 46 (1986)174, 491–516 · Zbl 0601.65060
[11] Chistyakov, V. P.: K metodam resheniya singulyarnykh linejnykh sistem obyknovennykh differentsial’nykh uravnenij. - In: Vyrozhdennye sistemy obyknovennykh differentsial’nykh uravnenij/ ed. Boyarintsev, Yu. S., Novosibirsk: Nauka, 1982, 37–65
[12] Campbell, S. L.: The numerical solution of the higher index linear time varying singular systems of differential equations. - SIM J. Sci. Stat. Comp. 6(1985)2, 334–348 · Zbl 0664.65084
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