Geodesic
Preservation of stability type of difference schemes when solving stiff differential algebraic equations
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 443-456 
V. F. Chistyakov. Preservation of stability type of difference schemes when solving stiff differential algebraic equations. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 443-456. http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a7/
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     title = {Preservation of stability type of difference schemes when solving stiff differential algebraic equations},
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     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Implicit methods applied to the numerical solution of systems of ordinary differential equations (ODEs) with an identically singular matrix multiplying the derivative of the sought-for vector-function are considered. The effects produced by losing $L$-stability of a classical implicit Euler scheme when solving such stiff systems are discussed.

[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, SIAM, Philadelphia, 1996 | MR | Zbl

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

[3] Chistyakov V. F., “Primenenie raznostnykh metodov dlya resheniya lineinykh sistem, ne razreshennykh otnositelno proizvodnykh”, Metody optimizatsii i ikh prilozheniya, SEI SO AN SSSR, Irkutsk, 1982, 56–60

[4] Loginov A. A., “Podkhod k postroeniyu paketa prikladnykh programm chislennogo integrirovaniya kraevykh zadach dlya sistem obyknovennykh differentsialnykh uravnenii”, Pakety prikladnykh programm. Metody i razrabotki, Nauka, Novosibirsk, 1981, 112–119

[5] Maerz R., “Differential algebraic systems anew”, Applied Numerical Mathematics, 42 (2002), 327–338 | MR

[6] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1990 | MR

[7] Godunov S. K., Ryabenkii V. S., Raznostnye skhemy, Nauka, M., 1977 | MR

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

[9] Boyarintsev Yu. E., Korsukov V. M., “Primenenie raznostnykh metodov k resheniyu regulyarnykh sistem obyknovennykh differentsialnykh uravnenii”, Voprosy prikladnoi matematiki, SEI SO AN SSSR, Irkutsk, 1975, 140–152

[10] Fedorenko R. P., Vvedenie v vychislitelnuyu fiziku, 2 izd., ispr. i dop., Izdatelskii dom “Intellekt”, Dolgoprudnyi, 2008

[11] Chistyakov V. F., O metodakh chislennogo resheniya i issledovaniya singulyarnykh sistem obyknovennykh differentsialnykh uravnenii, Dis. $\dots$ kand. fiz.-mat. nauk, Novosibirsk, 1985

[12] Chistyakov V. F., “O singulyarnykh sistemakh obyknovennykh differentsialnykh uravnenii i ikh integralnykh analogakh”, Funktsii Lyapunova i ikh primenenie, Hauka. Sibirskoe otd-nie, Novosibirsk, 1987, 231–239