Geodesic
Numerical solution of linear differential-algebraic systems of partial differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1530-1544 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A linear differential-algebraic system of partial differential equations of an arbitrary index is examined. The index of a differential-algebraic system is determined by the maximum degree (over the corresponding domain) of the elementary divisors corresponding to the zero and infinite roots of the characteristic polynomial of the matrix pencil constructed from the coefficients of this system. An iterative algorithm for the numerical solution of a differential-algebraic system is proposed. It is based on a special splitting of the associated matrix pencil and an application of the method of successive approximations to the split system. The stability of this method is shown, and its efficiency is demonstrated through test examples. 
@article{ZVMMF_2015_55_9_a8,
     author = {S. V. Gaidomak},
     title = {Numerical solution of linear differential-algebraic systems of partial differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1530--1544},
     year = {2015},
     volume = {55},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a8/}
}
TY  - JOUR
AU  - S. V. Gaidomak
TI  - Numerical solution of linear differential-algebraic systems of partial differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2015
SP  - 1530
EP  - 1544
VL  - 55
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a8/
LA  - ru
ID  - ZVMMF_2015_55_9_a8
ER  - 
%0 Journal Article
%A S. V. Gaidomak
%T Numerical solution of linear differential-algebraic systems of partial differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2015
%P 1530-1544
%V 55
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a8/
%G ru
%F ZVMMF_2015_55_9_a8
S. V. Gaidomak. Numerical solution of linear differential-algebraic systems of partial differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 9, pp. 1530-1544. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_9_a8/

[1] Bormotova O. V., Chistyakov V. F., “O metodakh chislennogo resheniya i issledovaniya sistem ne tipa Koshi–Kovalevskoi”, Zh. vychisl. matem. i matem. fiz., 4:8 (2004), 1380–1387

[2] Gaidomak S. V., “Ob odnoi kraevoi zadache dlya lineinoi parabolicheskoi sistemy pervogo poryadka”, Zh. vychisl. matem. i matem. fiz., 54:4 (2014), 73–83

[3] Gaidomak S. V., “Ob ustoichivosti neyavnoi raznostnoi skhemy dlya lineinoi differentsialno-algebraicheskoi sistemy uravnenii v chastnykh proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 50:4 (2010), 707–717 | MR | Zbl

[4] Gaidomak S. V., “Ob ustoichivosti neyavnoi splain-kollokatsionnoi raznostnoi skhemy dlya lineinykh differentsialno-algebraicheskikh uravnenii s chastnymi proizvodnymi”, Zh. vychisl. matem. i matem. fiz., 53:9 (2013), 44–63

[5] Marchuk G. I., Metody vychislitelnoi matematiki, Fizmatlit, M., 1977

[6] Kalitkin H. H., Chislennye metody, Nauka, M., 1978 | MR

[7] Gaidomak S. V., “O kanonicheskoi strukture puchka vyrozhdennykh matrits-funktsii”, Izvestiya vuzov. Matematika, 2012, no. 2, 23–33

[8] Chistyakov V. F., Algebro-differentsialnye operatory s konechnomernym yadrom, Sib. izdat. firma RAN “Nauka”, Novosibirsk, 1996 | MR

[9] Berezin I. S., Zhidkov N. P., Metody vychislenii, v. 1, Nauka, M., 1966

[10] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Libpokom, M., 2009

[11] Lankaster P., Teoriya matrits, Nauka, M., 1982 | MR

[12] Verbitskii B. V., “Odno globalnoe svoistvo matrits-funktsii, zavisyaschikh ot neskolkikh peremennykh”, Izvestiya vuzov. Matematika, 1978, no. 1(188), 8–17

[13] Voevodin V. V., Vychislitelnye osnovy lineinoi algebry, Fizmatlit, M., 1977 | MR

[14] Kublanovskaya V. N., “Algoritm-AV i ego svoistva”, Zap. nauchn. sem. LOMI, 102, 1980, 42–60 | MR | Zbl

[15] Kublanovskaya V. N., “O nekotorykh modifikatsiyakh algoritma AV”, Zap. nauchn. sem. LOMI, 111, 1981, 117–136 | MR | Zbl