Geodesic
The global error of one-step solution methods for stiff problems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 80-89.

Voir la notice de l'article provenant de la source Math-Net.Ru

We propose a new technique for estimating the global error of one-step solution methods for stiff systems. We adduce results of computations which confirm the reliability and efficiency of the error estimate.
Keywords: stiff problem, numerical method, global error. 
@article{IVM_2011_6_a9,
     author = {E. A. Novikov},
     title = {The global error of one-step solution methods for stiff problems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--89},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a9/}
}
TY  - JOUR
AU  - E. A. Novikov
TI  - The global error of one-step solution methods for stiff problems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 80
EP  - 89
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_6_a9/
LA  - ru
ID  - IVM_2011_6_a9
ER  - 
%0 Journal Article
%A E. A. Novikov
%T The global error of one-step solution methods for stiff problems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 80-89
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_6_a9/
%G ru
%F IVM_2011_6_a9
E. A. Novikov. The global error of one-step solution methods for stiff problems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 80-89. http://geodesic.mathdoc.fr/item/IVM_2011_6_a9/

[1] Novikov E. A., Babushok V. I., “Kombinirovannyi chislennyi algoritm rascheta kinetiki vzryvnykh protsessov”, Fizika goreniya i vzryva, 26:4 (1990), 85–93

[2] Byrne G. D., Hindmarsh A. C., “Stiff ODE solvers: a review of current and comming attractions”, J. Comput. Physics, 70 (1986), 1–62 | DOI | MR

[3] Artemev S. S., Demidov G. V., “Algoritm peremennogo poryadka i shaga dlya chislennogo resheniya zhestkikh sistem ODU”, DAN SSSR, 238:3 (1978), 517–520 | MR

[4] Demidov G. V., Novikov E. A., “O kontrole tochnosti yavnykh formul tipa Runge–Kutta vtorogo i tretego poryadkov approksimatsii s pomoschyu formul bolee nizkogo poryadka”, Chisl. metody mekh. splosh. sredy, 15:6 (1984), 59–74 | MR

[5] Shtetter Kh., Analiz metodov diskretizatsii dlya obyknovennykh differentsialnykh uravnenii, Mir, M., 1978 | MR

[6] Khairer E., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Zhestkie i differentsialno-algebraicheskie zadachi, Mir, M., 1999

[7] Novikov E. A., Yavnye metody dlya zhestkikh sistem, Nauka, Novosibirsk, 1997 | MR

[8] Novikov E. A., Shitov Yu. A., Shokin Yu. I., “Odnoshagovye bezyteratsionnye metody resheniya zhestkikh sistem”, DAN SSSR, 301:6 (1988), 1310–1314 | MR

[9] Novikov E. A., “Postroenie algoritma integrirovaniya zhestkikh sistem differentsialnykh uravnenii na neodnorodnykh skhemakh”, DAN SSSR, 278:2 (1984), 272–275 | MR | Zbl

[10] Novikov E. A., Shitov Yu. A., Issledovanie $(m,k)$-metodov resheniya zhestkikh sistem s odnim i dvumya vychisleniyami pravoi chasti, preprint VTs SO RAN No 15, Krasnoyarsk, 1987, 41 pp.

[11] Babushok V. I., Marin D. V., Namyatov G. V. i dr., “Dinamika vydeleniya tepla pri destruktivnom khlorirovanii khloruglevodorodov”, Khim. promyshlennost, 1994, no. 2, 11–19