Geodesic
On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 8, pp. 1180-1189 Cet article a éte moissonné depuis la source Math-Net.Ru

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G. Yu. Kulikov. On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 8, pp. 1180-1189. http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_8_a3/

[1] Grodinz F., Teoriya regulirovaniya i biologicheskie sistemy, Mir, M., 1966

[2] Guyton A. C., Coleman T. G., Gardner H. J., “Circulation: overall regulation”, Ann. Rev. Phisiol., 34 (1972), 13–41 | DOI

[3] Ikeda N., Marumo F., Shiratare M., Sato T., “A model of overall regulation of body fluids”, Ann. Biomed. Engng., 7 (1979), 135–166 | DOI

[4] Petzold L. R., Lotstedt P., “Numerical solution of nonlinear differential equations with algebraic constrains. II: Practical implications”, SIAM J. Sci. Statist. Comput., 7 (1986), 720–733 | DOI | MR | Zbl

[5] Boyarintsev Yu. E., Danilov V. A., Loginov A. A., Chistyakov V. F., Chislennye metody resheniya singulyarnykh sistem, Nauka, Novosibirsk, 1989 | Zbl

[6] Belash V. O., Glebov A. L., Maryashkin N. Ya., Ovchinnikov E. E., Reshenie differentsialno-algebraicheskikh sistem skhemotekhnicheskogo analiza BIS, VTs AN SSSR, M., 1991

[7] Nerreter V., Raschet elektricheskikh tsepei na personalnoi EVM, Energoatomizdat, M., 1991

[8] Boyarintsev Yu. E., Metody resheniya nepreryvnykh i diskretnykh zadach dlya singulyarnykh sistem uravnenii, Nauka, Novosibirsk, 1996 | MR | Zbl

[9] Hairer E., Wanner G., Solving ordinary differential equations, v. II, Stiff and differential-algebraic problems, Springer, Berlin, 1996 | MR | Zbl

[10] Gear C. W., “Differential-algebraic equations index transformations”, SIAM J. Sci. Statist. Comput., 9 (1988), 39–47 | DOI | MR | Zbl

[11] Kulikov G. Yu., “O chislennom reshenii avtonomnoi zadachi Koshi s algebraicheskoi svyazyu na fazovye peremennye (nevyrozhdennyi sluchai)”, Vestn. MGU. Ser. matem., mekhan., 1993, no. 3, 10–14 | MR

[12] Brenan K. E., Campbell S. L., Petzold L. R., Numerical solution of initial-value problems in differential-algebraic equations, North-Holland, New York etc., 1989 | MR | Zbl

[13] Hairer E., Lubich Ch., Roche M., The numerical solution of differential-algebraic systems by Runge–Kutta methods, Lect. note math., 1409, Springer, Berlin, 1989 | MR | Zbl

[14] Kulikov G. Yu., “Chislennoe reshenie avtonomnoi zadachi Koshi s algebraicheskoi svyazyu na fazovye peremennye”, Zh. vychisl. matem. i matem. fiz., 33:4 (1993), 522–540 | MR | Zbl

[15] Kulikov G. Yu., “Prakticheskaya realizatsiya i effektivnost chislennykh metodov resheniya zadachi Koshi s algebraicheskoi svyazyu”, Zh. vychisl. matem. i matem. fiz., 34:11 (1994), 1617–1631 | MR | Zbl

[16] Kulikov G. Yu., “Teoremy skhodimosti dlya iterativnykh metodov Runge-Kutty s postoyannym shagom integrirovaniya”, Zh. vychisl. matem. i matem. fiz., 36:8 (1996), 73–89 | MR | Zbl

[17] Kulikov G. Yu., “Numerical methods solving the semi-explicit differential-algebraic equations by implicit mtiltistep fixed stepsize methods”, Korean J. Comput. and Appl. Math., 4:2 (1997), 281–318 | MR | Zbl

[18] Kulikov G. Yu., “Chislennoe reshenie zadachi Koshi dlya sistemy differentsialno-algebraicheskikh uravnenii s pomoschyu neyavnykh metodov Runge-Kutty s netrivialnym prediktorom”, Zh. vychisl. matem. i matem. fiz., 38:1 (1998), 68–84 | MR | Zbl

[19] Kuznetsov E. B., Shalashilin V. I., “Zadacha Koshi kak zadacha prodolzheniya resheniya po parametru”, Zh. vychisl. matem. i matem. fiz., 33:12 (1993), 1792–1805 | MR | Zbl

[20] Kuznetsov E. B., Shalashilin V. I., “Reshenie differentsialno-algebraicheskikh uravnenii s vyborom nailuchshego argumenta”, Zh. vychisl. matem. i matem. fiz., 37:6 (1997), 711–722 | MR | Zbl

[21] Shalashilin V. I., Kuznetsov E. B., Metod prodolzheniya resheniya po parametru i nailuchshaya parametrizatsiya, Editorial URSS, M., 1999 | MR

[22] Ortega Dzh., Reinboldt V., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1975 | MR

[23] Kulikov G. Yu., “Asimptoticheskie otsenki pogreshnosti metoda prostykh iteratsii, moditsifitsirovannogo i obobschennogo metodov Nyutona”, Matem. zametki, 63:4 (1998), 562–571 | MR | Zbl