Geodesic
Regularization of differential-algebraic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2181-2193 Cet article a éte moissonné depuis la source Math-Net.Ru

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Linear systems of ordinary differential equations with an identically singular or rectangular matrix multiplying the derivative of the unknown vector function are numerically solved by applying the least squares method and Tikhonov regularization. The deviation of the solution of the regularized problem from the solution set of the original problem is estimated depending on the regularization parameter. 
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V. F. Chistyakov. Regularization of differential-algebraic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2181-2193. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a4/

[1] Brenan K. E., Campbell S. L., Petzold L. R., Numerical solution of initial-value problems in differential-algebraic equations, Classics in Applied Mathematics, 14, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996, 256 pp. | MR | Zbl

[2] Boyarintsev Yu. E., Chistyakov V. F., Algebro-differentsialnye sistemy. Metody resheniya i issledovaniya, Hauka, Novosibirsk, 1998 | MR

[3] Chistyakov V. F., “K metodam resheniya singulyarnykh lineinykh sistem obyknovennykh differentsialnykh uravnenii”, Vyrozhdennye sistemy obyknovennykh differents. ur-nii, Nauka, Novosibirsk, 1982, 37–66 | MR

[4] Bulatov M. V., Chistyakov V. F., “Reshenie algebro-differentsialnykh sistem metodom naimenshikh kvadratov”, Tr. XI mezhdunar. Baikalskoi shkoly-seminara (Baikal, 5–12 iyulya 1998 g.), v. 4, Irkutsk, 1998, 72–75

[5] Gorbunov V. K., “Metod normalnoi splain-kollokatsii”, Zh. vychisl. matem. i matem. fiz., 29:2 (1989), 212–224 | MR

[6] Gorbunov V. K., Petrischev V. V., “Razvitie metoda normalnoi splain-kollokatsii dlya lineinykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 43:8 (2003), 1161–1170 | MR

[7] Gorbunov V. K., Lutoshkin I. V., “The parametrization method in optimal control problems and differential algebraic equations”, J. Comput. Appl. Math., 185:2 (2006), 377–390 | DOI | MR | Zbl

[8] Gorbunov V. K., Sviridov V. Yu., “The method of normal splines for linear DAEs on the number semi-axis”, Appl. Numer. Math., 59:3–4 (2009), 656–670 | DOI | MR | Zbl

[9] Bulatov M. V., Gorbunov V. K., Martynenko Yu. V., Nguen Din Kong, “Variatsionnye podkhody k chislennomu resheniyu differentsialno-algebraicheskikh uravnenii”, Vychisl. tekhnologii, 15:5 (2010), 3–13 | Zbl

[10] Gantmakher F. R., Teoriya matrits, izd. 3-e, Nauka, M., 1966 | MR

[11] Boyarintsev Yu. E., Regulyarnye i singulyarnye sistemy lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, Novosibirsk, 1980 | MR | Zbl

[12] Chistyakov V. F., Algebro-differentsialnye operatory s konechnomernym yadrom, Hauka, Novosibirsk, 1996 | MR

[13] Campbell S. L., Petzold L. R., “Canonical forms and solvable singular sys of differential equations”, SIAM J. Alg. and Discrete Meth., 1983, no. 4, 517–521 | DOI | MR | Zbl

[14] Kunkel P., Mehrmann V., Differential-algebraic equations: analysis and numerical solution, European Math. Soc., 2006 | MR | Zbl

[15] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Izd-vo MGU, M., 1974

[16] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

[17] Godunov S. K., Uravneniya matematicheskoi fiziki, Nauka, M., 1971 | MR

[18] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl