Geodesic
On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 3, pp. 483-498 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A class of finite-difference schemes for solving ill-posed Cauchy problems for first-order linear differential equations with sectorial operators in Banach spaces is examined. Under various assumptions concerning the desired solution, time-uniform accuracy and error characteristics are obtained that refine and improve known estimates for these schemes. Some numerical results are presented. 
@article{ZVMMF_2012_52_3_a8,
     author = {A. B. Bakushinskii and M. M. Kokurin and M. Yu. Kokurin},
     title = {On a~class of finite-difference schemes for solving ill-posed {Cauchy} problems in {Banach} spaces},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {483--498},
     year = {2012},
     volume = {52},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_3_a8/}
}
TY  - JOUR
AU  - A. B. Bakushinskii
AU  - M. M. Kokurin
AU  - M. Yu. Kokurin
TI  - On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2012
SP  - 483
EP  - 498
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_3_a8/
LA  - ru
ID  - ZVMMF_2012_52_3_a8
ER  - 
%0 Journal Article
%A A. B. Bakushinskii
%A M. M. Kokurin
%A M. Yu. Kokurin
%T On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2012
%P 483-498
%V 52
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_3_a8/
%G ru
%F ZVMMF_2012_52_3_a8
A. B. Bakushinskii; M. M. Kokurin; M. Yu. Kokurin. On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 3, pp. 483-498. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_3_a8/

[1] Krein S.G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967

[2] Ivanov V.K., Melnikova I.V., Filinkov A.I., Differentsialno-operatornye uravneniya i nekorrektnye zadachi, Nauka, M., 1995

[3] Bakushinskii A.B., Kokurin M.Yu., Klyuchev V.V., “Ob otsenke skorosti skhodimosti i pogreshnosti raznostnykh metodov approksimatsii resheniya nekorrektnoi zadachi Koshi v banakhovom prostranstve”, Vychisl. metody i programmirovanie, 7 (2006), 163–171 | MR

[4] Lavrentev M.M., Romanov V.G., Shishatskii S.P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980

[5] Bakhvalov N.C., Zhidkov N.P., Kobelkov G.M., Chislennye metody, BINOM, M., 2007

[6] Babushka I., Vitasek E., Prager M., Chislennye protsessy resheniya differentsialnykh uravnenii, Mir, M., 1972

[7] Bakushinskii A.B., “Raznostnye metody resheniya nekorrektnykh zadach Koshi dlya evolyutsionnykh uravnenii v kompleksnom V-prostranstve”, Differents. ur-niya, 8:9 (1972), 1661–1668 | MR | Zbl

[8] Samarskii A.A., Vabischevich P.N., Chislennye metody resheniya obratnykh zadach matematicheskoi fiziki, Editorial URSS, M., 2004

[9] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972