On BDF-Based Multistep Schemes for Some Classes of Linear Differential-Algebraic Equations of Index at Most 2

Ascher, U., Petzold, L.: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM (1998)

Berger, T., Ilchmann, A.: On the standard canonical form of time-varying linear DAEs. Quarterly Appl. Math. 71(1), 69–87 (2013)

Bock, H.G., Schloder, J.P., Schulz, V.H.: Differential-algebraic equations and their connections to optimization. Heidelberg, Preprint 96-58 (SFB 359) (1996)

Boyarintsev, Yu.E.: Regular and Singular Systems of Ordinary Differential Equations. Nauka, Novosibirsk (1980). (in Russian)

Boyarintsev, Yu.E., Orlova, I.V.: Matrix Pencils and Differential-Algebraic Equations. Nauka Novosibirsk (2006). (in Russian)

Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia (1996)

Bulatov, M.V., Ming-Gong, L., Solovarova, L.S.: On first and second-order difference schemes for differential-algebraic equations of index at most two. Comput. Math. Math. Phys. 50(11), 1808–1817 (2010)

Chistyakov, V.F.: On expansion of linear systems unsolved relative to the derivatives. Preprint No. 5, Irkutsk Computing Center, Siberian Branch, USSR Academy of Sciences, Irkutsk (1986). (in Russian)

Chistyakov, V.F.: Differential-Algebraic Operators with Finite-Dimensional Kernels. Nauka, Novosibirsk (1996). (in Russian)

Dokchan, R.: Numerical Integration of Differential-Algebraic Equations with Harmless Critical Point. Ph.D. thesis. Humboldt-University of Berlin (2011)

Griepentrog, E., März, R.: Differential-algebraic equations and their numerical treatment. Teubner. Texte Zur. Math. Band, 88 (1986)

Hairer, E., Lubich, C., Roche, M.: The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods. Lecture Notes in Mathematics, 1409. Springer Verlag (1989)

Hairer, E., Norsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer-Verlag, Berlin (1988)

Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential Algebraic Problems. Springer-Verlag, Berlin (1996)

Higueras, I., März, R., Tischendorf, C.: Stability preserving integration of index-1 DAEs. Appl. Num. Math. 45, 175–200 (2003)

Higueras, I., März, R., Tischendorf, C.: Stability preserving integration of index-2 DAEs. Appl. Num. Math. 45, 201–229 (2003)

Kunkel, P., Mehrmann, V.: Differential-Algebraic Equations. Analysis and Numerical Solution. EMS Publishing House, Zürich, Switzerland (2006)

Kunkel, P., Mehrmann, V.: Stability properties of differential-algebraic equations and spin-stabilized discretizations. Electr. Trans. Numer. Anal. 26, 385–420 (2007)

Lamour, R., März, R., Tischendorf, C.: Differential-Algebraic Equations: A Projector Based Analysis. Springer (2013)

Linh, V.H., Mehrmann, V.: Efficient integration of strangeness-free non-stiff differential-algebraic equations by half-explicit methods. J. Comp. Appl. Math. 262, 346–360 (2014)

März, R.: Differential-algebraic systems anew. Appl. Numer. Math. 42, 315–335 (2002)