Geodesic
Difference methods for solving non-local boundary value problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 3, pp. 265-287.

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

This paper deals with the to boundary value problems for pseudoparabolic equations of fractional order with the Bessel operator with variable coefficients with non-local boundary conditions of the integral type and difference methods for their solutions. To solve the considered problems a priori estimates in differential and difference interpretations are obtained, which means the uniqueness and stability of solutions by initial data and the right-hand side, as well as the convergence of the solution of the difference problem to the solution of the corresponding differential problem. 
@article{SJVM_2020_23_3_a2,
     author = {M. K. Beshtokov},
     title = {Difference methods for solving non-local boundary value problems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {265--287},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a2/}
}
TY  - JOUR
AU  - M. K. Beshtokov
TI  - Difference methods for solving non-local boundary value problems
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2020
SP  - 265
EP  - 287
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a2/
LA  - ru
ID  - SJVM_2020_23_3_a2
ER  - 
%0 Journal Article
%A M. K. Beshtokov
%T Difference methods for solving non-local boundary value problems
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2020
%P 265-287
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a2/
%G ru
%F SJVM_2020_23_3_a2
M. K. Beshtokov. Difference methods for solving non-local boundary value problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 3, pp. 265-287. http://geodesic.mathdoc.fr/item/SJVM_2020_23_3_a2/

[1] E. S. Dzektser, “Uravneniya dvizheniya podzemnyh vod so svobodnoi poverhnost'yu v mnogosloinyh sredah”, Dokl. AN SSSR, 220:3 (1975), 540–543 | Zbl

[2] L. I. Rubinshtein, “K voprosu o protsesse rasprostraneniya tepla v geterogennyh sredah”, Izv. AN SSSR. Ser. geogr. i geofiz., 12:1 (1948), 27–45 | MR

[3] T. W. Ting, “A cooling process according to two-temperature theory of heat conduction”, J. Math. Anal. Appl., 45:9 (1974), 23–31 | DOI | MR | Zbl

[4] M. Hallaire, “Le potentiel efficace de l'eau dans le sol en régime de desséchement”, L'eau et la production vegetale, INRA, Paris, 1964, 27–62

[5] A. F. Chudnovskii, Teplofizika pochv, Nauka, M., 1976

[6] R. L. Begli, P. Dzh. Tovik, “Differentsial'noe ischislenie, osnovannoe na proizvodnyh drobnogo poryadka novyi podhod k raschetu konstruktsii s vyazko-uprugim dempfirovaniem”, Aerokosmicheskaya tekhnika, 2:2 (1984), 84–93

[7] O. Yu. Dinariev, “Fil'tratsiya v treschinovatoi srede s fraktal'noi geometriei treschin”, Izv. AN SSSR. Mekhanika zhidkosti i gaza, 5 (1990), 66–70 | MR | Zbl

[8] L. O-Shaughnessy, “Problem 433”, Amer. Math. Month., 25 (1918), 172–173 | DOI | MR

[9] S. Mandelbrojt, “Sulla generalizzazione del calcolo clelle variazione”, Atti Reale Accad. Naz. Lincei. Rend Cl. sei., fis. mat. e natur. Ser. 6, 1 (1925), 151–156 | Zbl

[10] A. B. Mal'shakov, “Uravneniya gidrodinamiki dlya poristyh sred so strukturoi porovogo prostranstva, obladayuschei fraktal'noi geometriei”, IFZh, 62:3 (1992), 405–410 | MR

[11] D. Shefer, K. Kefer, “Fraktaly v fizike”, Tr. 6-go Mezhdunar. simpoz. po fraktalam v fizike (9–12 iyunya 1985 g.. Italiya), MTSTF, Triest, 1988, 62–71

[12] S. G. Samko, A. A. Kilbas, O. I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye ih prilozheniya, Minsk, 1987

[13] A. M. Nahushev, Elementy drobnogo ischisleniya i ih primeneniya, NII PMA KBNTS RAN, Nal'chik, 2000

[14] K. V. Chukbar, “Stohasticheskii perenos i drobnye proizvodnye”, ZhETF, 108:5(11) (1995), 1875–1884

[15] A. N. Kochubei, “Diffuziya drobnogo poryadka”, Diff. uravneniya, 26:4 (1990), 660–670 | MR | Zbl

[16] S. Yu. Bedanokova, “Uravnenie dvizheniya pochvennoi vlagi i matematicheskaya model' vlagosoderzhaniya pochvennogo sloya, osnovannaya na uravnenii Allera”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya 4: Estestvenno-matematicheskie i tekhnicheskie nauki, 4 (2007), 68–71

[17] A. A. Alihanov, “Apriornye otsenki reshenii kraevyh zadach dlya uravnenii drobnogo poryadka”, Diff. uravneniya, 46:5 (2010), 660–666 | MR | Zbl

[18] A. A. Alikhanov, “A new difference scheme for the time fractional diffusion equation”, J. of Computational Physics, 280 (2015), 424–438 | DOI | MR | Zbl

[19] F. I. Taukenova, M. H. Shkhanukov-Lafishev, “Raznostnye metody resheniya kraevyh zadach dlya differentsial'nyh uravnenii drobnogo poryadka”, Zhurn. vychisl. matem. i mat. fiziki, 46:10 (2006), 1871–1881 | MR

[20] A. I. Kozhanov, “Ob odnoi nelokal'noi kraevoi zadache s peremennymi koeffitsientami dlya uravnenii teploprovodnosti i Allera”, Diff. uravneniya, 40:6 (2004), 763–774 | MR | Zbl

[21] E. V. Venitsianov, R. N. Rubinshtein, Dinamika sorbtsii iz zhidkih sred, Nauka, M., 1983

[22] A. A. Samarskii, Teoriya raznostnyh skhem, Nauka, M., 1977

[23] M. H. Beshtokov, “O chislennom reshenii nelokal'noi kraevoi zadachi dlya vyrozhdayuschegosya psevdoparabolicheskogo uravneniya”, Diff. uravneniya, 52:10 (2016), 1393–1406 | MR | Zbl

[24] M. H. Beshtokov, “Raznostnyi metod resheniya nelokal-noi kraevoi zadachi dlya vyrozhdayuschegosya psevdoparabolicheskogo uravneniya tret'ego poryadka s peremennymi koeffitsientami”, Zhurn. vychisl. matem. i mat. fiziki, 56:10 (2016), 1780–1794 | MR | Zbl

[25] M. H. Beshtokov, “Lokal'nye i nelokal'nye kraevye zadachi dlya vyrozhdayuschihsya i nevyrozhdayuschihsya psevdoparabolicheskih uravnenii s drobnoi proizvodnoi Rimana–Liuvillya”, Diff. uravneniya, 54:6 (2018), 763–778 | MR | Zbl

[26] H. Caputo, “Linear models of dissipation whose Q is almost frequency independent II”, Geophys J. Royal Astronom. Soc., 13 (1967), 529–539 | DOI

[27] A. N. Gerasimov, “Obobschenie lineinyh zakonov deformatsii i ih prilozhenie k zadacham vnutrennego treniya”, Prikladnaya matematika i mekhanika, 12 (1948), 251–260 | Zbl

[28] D. Li, H. L. Liao, W. Sun, J. Wang, J. Zhang, “Analysis of L1-Galerkin FEMs for timefractional nonlinear parabolic problems”, Commun. Comput. Phys., 24:1 (2018), 86–109 | MR

[29] A. A. Samarskii, A. V. Gulin, Ustoichivost' raznostnyh skhem, Nauka, M., 1973

[30] D. K. Faddeev, V. N. Faddeeva, Vychislitel'nye metody lineinoi algebry, Fizmatgiz, M., 1960 | MR

[31] M. H. Beshtokov, “Differencial'nye i raznostnye kraevye zadachi dlya nagruzhennyh psevdoparabolicheskih uravnenij tret'ego poryadka i raznostnye metody ih chislennoj realizacii”, Zhurn. vychisl. matem. i mat. fiziki, 57:12 (2017), 2021–2041 | MR | Zbl