Geodesic
About one explicit-difference scheme for solving the plane problem for two-component medium
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 3-11 
V. Cheban; I. Naval. About one explicit-difference scheme for solving the plane problem for two-component medium. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2004), pp. 3-11. http://geodesic.mathdoc.fr/item/BASM_2004_2_a0/
@article{BASM_2004_2_a0,
     author = {V. Cheban and I. Naval},
     title = {About one explicit-difference scheme for solving the plane problem for two-component medium},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {3--11},
     year = {2004},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2004_2_a0/}
}
TY  - JOUR
AU  - V. Cheban
AU  - I. Naval
TI  - About one explicit-difference scheme for solving the plane problem for two-component medium
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2004
SP  - 3
EP  - 11
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/BASM_2004_2_a0/
LA  - en
ID  - BASM_2004_2_a0
ER  - 
%0 Journal Article
%A V. Cheban
%A I. Naval
%T About one explicit-difference scheme for solving the plane problem for two-component medium
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2004
%P 3-11
%N 2
%U http://geodesic.mathdoc.fr/item/BASM_2004_2_a0/
%G en
%F BASM_2004_2_a0

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

The finite-difference scheme for plane dynamical problem of the theory of elasticity of two-component medium in displacements is obtained. The stability of this scheme by means of Niemann conditions is studied. Is found the maximal time step in dependence on the space step for which the stability is kept.

[1] Biot M. A., “General theory of three-dimensional consolidation”, J. Appl. Phys., 12 (1941)

[2] Bio M. A., “Teoriya uprugosti i konsolidatsii anizotropnoi poristoi sredy”, Mekhanika, Sbornik perevodov i obzorov inostrannoi periodicheskoi literatury, no. 1, Inostr. lit., Moskva, 1956, 140–146

[3] Bio M. A., “Mekhanika deformirovaniya i rasprostraneniya akusticheskikh voln v poristoi srede”, Mekhanika, Sbornik periodicheskoi literatury, Inostr. lit., Moskva, 1963, 103–135

[4] Frenkel Ya. I., “K teorii seismicheskikh i seismoelektricheskikh yavlenii vo vlazhnoi pochve”, Izv. AN SSSR. Ser. geograf. i geofiz., 8:4 (1944), 133–149 | MR

[5] Rakhmatulin Kh. A., “Osnovy gazodinamiki vzaimopronikayushchikh dvizhenii szhimaemykh sred”, PMM, 20:2 (1956), 184–195

[6] Filippov I. G., “Dinamicheskaya teoriya otnositel'nogo techeniya mnogokomponentnykh sred”, Prikladnaya mekhanika, 7:10 (1971), 92–99

[7] Filippov I. G., Cheban V. G., Neustanovivshiesya dvizheniya sploshnykh szhimaemykh sred, Shtiintsa, Kishinev, 1973 | MR

[8] Kosachevskii L. Ya., “O rasprostranenii uprugikh voln v dvukhkomponetnykh sredakh”, Prikladnaya matematika i mekhanika, 23:6 (1959), 1115–1123 | Zbl

[9] Mardonov B., Ibraimov O., “O metode kharakteristik v teorii dvizheniya poristouprugoi sredy”, Materialy V vses. simp. po rasprostraneniyu uprugikh i uprugoplasticheskikh voln, Alma-Ata, 1973

[10] Nikolaevskii V. N., “Nelineinoe priblizhenie k mekhanike uplotnyaemykh sred”, Izv. AN SSSR, OTN mekh. i mashin, 1962, no. 5, 59–62 | MR

[11] Erzhanov Zh. S., Karimbaev T. D., Baiteliev T. B., Dvumernye volny napryazhenii v odnorodnykh i strukturno-neodnorodnykh sredakh, Nauka, Alma-Ata, 1983

[12] Dzhons D. R., “Rasprostranenie impul'sa v poristo-uprugom tele”, Prikladnaya mekhanika, 1969, no. 4, 237–238

[13] Fatt J., “The Biot-Welles elastic coefficients for Sandstones”, J. Appl. Mech., 26:1 (1959), 296–297

[14] Richtmaier R. D., The different methods of the solutions of regional problems, Inostr. lit., Moskva, 1960