März, Roswitha Some new results concerning index-3 differential-algebraic equations. (English) Zbl 0672.34006 J. Math. Anal. Appl. 140, No. 1, 177-199 (1989). A class of nonlinear nontransferable differential-algebraic equations \(f(x'(t),x(t),t)=0\), which contains both the linear equations having the global index 3 and the nonlinear index-3 equations in the understandung of Gear and Petzold, is characterized. For such “index-3-tractable” equations a matrix criterion in terms of the partial Jacobians \(f'_ y(y,x,t)\), \(f'_ x(y,x,t)\) is given. Existence and uniqueness statements are proved. In particular, it is shown how to formulate initial conditions. Reviewer: R.März Cited in 2 ReviewsCited in 6 Documents MSC: 34A30 Linear ordinary differential equations and systems Keywords:higher index equation; solvability; nonlinear nontransferable differential-algebraic equations PDFBibTeX XMLCite \textit{R. März}, J. Math. Anal. Appl. 140, No. 1, 177--199 (1989; Zbl 0672.34006) Full Text: DOI References: [1] Dolezal, V., Zur Dynamik der Linearsysteme, Acta Tech., 9-33 (1960) [2] Gantmakher, F. R., Teoriya Matrits (1966), Nauka: Nauka Moscow · Zbl 0666.15002 [3] Gear, C. W.; Petzold, L. R., ODE methods for the solution of differential/algebraic systems, SIAM J. Numer. Anal., 2, No. 4, 716-728 (1984) · Zbl 0557.65053 [4] Griepentrog, E.; März, R., Differential-algebraic equations and their numerical treatment, Teubner-Texte zur Math., 88 (1986) · Zbl 0629.65080 [5] März, R., Results in Mathematics, 15, 149-171 (1989) [6] März, R., On correctness and numerical treatment of boundary value problems in DAE’s, Zh. Vychisl. Mat. i Mat. Fiz., 26, 50-64 (1986) · Zbl 0602.65062 [7] März, R., On initial value problems in Differential-algebraic equations and their numerical treatment, Computing, 35, 13-37 (1985) · Zbl 0554.65050 [8] Gear, C. W.; Petzold, L. R., Differential/algebraic systems and matrix pencils, (Kagström, B.; Ruhe, A., Matrix Pencils. Matrix Pencils, Lecture Notes in Mathematics, Vol. 973 (1983), Springer-Verlag: Springer-Verlag Berlin), 75-89 · Zbl 0494.65038 [9] Lötstedt, P.; Petzold, L., Numerical solution of nonlinear differential equations with algebraic constraints, Math. Comp., 46, 491-516 (1986) · Zbl 0601.65060 [10] Brenan, K. E.; Enquist, B. E., Backward Difference Approximations of Nonlinear Differential-Algebraic Equations (1985), The Aerospace Corporation: The Aerospace Corporation El Segundo, CA This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.