Geodesic
Stable difference schemes for certain parabolic equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1186-1193 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In some applications, boundary value problems for second-order parabolic equations with a special nonself-adjoint operator have to be solved approximately. The operator of such a problem is a weighted sum of self-adjoint elliptic operators. Unconditionally stable two-level schemes are constructed taking into account that the operator of the problem is not self-adjoint. The possibilities of using explicit-implicit approximations in time and introducing a new sought variable are discussed. Splitting schemes are constructed whose numerical implementation involves the solution of auxiliary problems with self-adjoint operators. 
@article{ZVMMF_2014_54_7_a7,
     author = {N. M. Afanas'eva and P. N. Vabishchevich},
     title = {Stable difference schemes for certain parabolic equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1186--1193},
     year = {2014},
     volume = {54},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a7/}
}
TY  - JOUR
AU  - N. M. Afanas'eva
AU  - P. N. Vabishchevich
TI  - Stable difference schemes for certain parabolic equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 1186
EP  - 1193
VL  - 54
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a7/
LA  - ru
ID  - ZVMMF_2014_54_7_a7
ER  - 
%0 Journal Article
%A N. M. Afanas'eva
%A P. N. Vabishchevich
%T Stable difference schemes for certain parabolic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 1186-1193
%V 54
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a7/
%G ru
%F ZVMMF_2014_54_7_a7
N. M. Afanas'eva; P. N. Vabishchevich. Stable difference schemes for certain parabolic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 7, pp. 1186-1193. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_7_a7/

[1] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989

[2] Khabner P., Angermann L., Numerical methods for elliptic and parabolic partial differential equations, Springer, Berlin, 2003

[3] Samarskii A. A., Gulin A. V., Ustoichivost raznostnykh skhem, Nauka, M., 1973

[4] Samarskii A. A., Matus P. P., Vabishchevich P. N., Difference schemes with operator factors, Kluwer, London, 2002

[5] Morton K. W., Kellogg R. B., Numerical solution of convection-diffusion problems, Chapman Hall, London, 1996

[6] Samarskii A. A., Vabischevich P. N., Additivnye skhemy dlya zadach matematicheskoi fiziki, Nauka, M., 1999

[7] Hundsdorfer W. H., Verwer J. C., Numerical solution of time-dependent advection-diffusion-reaction equations, Springer, Berlin, 2003

[8] Vabischevich P. N., Vasileva M. V., “Yavno-neyavnye skhemy dlya zadach konvektsii-diffuzii-reaktsii”, Sib. zhurnal vychisl. matem., 15:4 (2012), 359–369

[9] Afanaseva N. M., Vabischevich P. N., Vasileva M. V., “Bezuslovno ustoichivye skhemy dlya zadach konvektsii-diffuzii”, Izvestiya VUZov. Matematika, 2013, no. 3, 3–15

[10] Peaceman D. W., Fundamentals of numerical reservoir simulation, Elsevier, Amsterdam, 2000

[11] Aziz K., Settari A., Petroleum reservoir simulation, Applied Sci. Pub., London, 1979

[12] Vabishchevich P. N., Vasil'eva M. V., “Iterative solution of the pressure problem for the multiphase filtration”, Math. Modelling and Analys., 17:4 (2012), 532–549 | DOI

[13] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978

[14] Saad Y., Iterative methods for sparse linear systems, SIAM, Philadelphia, 2003

[15] Vabischevich P. N., “Yavno-neyavnye vychislitelnye algoritmy dlya zadach mnogofaznoi filtratsii”, Matem. modelirovanie, 22:4 (2010), 118–128

[16] Marchuk G. I., Metody rasschepleniya, Nauka, M., 1988

[17] Vabischevich P. N., Additivnye operatorno-raznostnye skhemy (skhemy rasschepleniya), URSS, M., 2013