Geodesic
Numerical diagnostics of solution blowup in differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 111-121 
A. A. Belov. Numerical diagnostics of solution blowup in differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 1, pp. 111-121. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a9/
@article{ZVMMF_2017_57_1_a9,
     author = {A. A. Belov},
     title = {Numerical diagnostics of solution blowup in differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {111--121},
     year = {2017},
     volume = {57},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a9/}
}
TY  - JOUR
AU  - A. A. Belov
TI  - Numerical diagnostics of solution blowup in differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 111
EP  - 121
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a9/
LA  - ru
ID  - ZVMMF_2017_57_1_a9
ER  - 
%0 Journal Article
%A A. A. Belov
%T Numerical diagnostics of solution blowup in differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 111-121
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_1_a9/
%G ru
%F ZVMMF_2017_57_1_a9

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

New simple and robust methods have been proposed for detecting poles, logarithmic poles, and mixed-type singularities in systems of ordinary differential equations. The methods produce characteristics of these singularities with a posteriori asymptotically precise error estimates. This approach is applicable to an arbitrary parametrization of integral curves, including the arc length parametrization, which is optimal for stiff and ill-conditioned problems. The method can be used to detect solution blowup for a broad class of important nonlinear partial differential equations, since they can be reduced to huge-order systems of ordinary differential equations by applying the method of lines. The method is superior in robustness and simplicity to previously known methods.

[1] Brakner K., Dzhorna S., Upravlyaemyi lazernyi sintez, Atomizdat, M., 1977

[2] Samarskii A. A., Galaktionov V. A., Kurdyumov S. P., Mikhailov A. P., Rezhimy s obostreniem v zadachakh dlya kvazilineinykh parabolicheskikh uravnenii, Nauka, M., 1987 | MR

[3] Sveshnikov A. G., Alshin A. B., Korpusov M. O., Pletner Yu. D., Lineinye i nelineinye uravneniya sobolevskogo tipa, Fizmatlit, M., 2007

[4] Alshina E. A., Kalitkin N. N., Koryakin P. V., “Diagnostika osobennostei tochnogo resheniya metodom sguscheniya setok”, Dokl. AN. Informatika, 404:3 (2005), 295–299 | Zbl

[5] Alshina E. A., Kalitkin N. N., Koryakin P. V., “Diagnostika osobennostei tochnogo resheniya pri raschetakh s kontrolem tochnosti”, Zh. vychisl. matem. i matem. fiz., 45:10 (2005), 1837–1847 | Zbl

[6] Kalitkin H. H., Alshin A. B., Alshina E. A., Rogov B. V., Vychisleniya na kvaziravnomernykh setkakh, Fizmatlit, M., 2005