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

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.

[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