Geodesic
A grid approximation of singularly perturbed quasilinear elliptic and parabolic equations which degenerate into equations without spatial derivatives
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 34 (1994) no. 11, pp. 1632-1651 Cet article a éte moissonné depuis la source Math-Net.Ru

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G. I. Shishkin. A grid approximation of singularly perturbed quasilinear elliptic and parabolic equations which degenerate into equations without spatial derivatives. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 34 (1994) no. 11, pp. 1632-1651. http://geodesic.mathdoc.fr/item/ZVMMF_1994_34_11_a6/

[1] Miller J. J. H., Shishkin G. I., “On the construction of uniformly convergent finite difference schemes for singularly perturbed problems for a quasi-linear elliptic equation”, Comput. Methods Bound. and Internat. Layers in Several Dimensions, Boole Press, Dublin, 1991, 103–118 | MR

[2] Shishkin G. I., “Setochnaya approksimatsiya singulyarno vozmuschennoi kraevoi zadachi dlya kvazilineinogo ellipticheskogo uravneniya v sluchae polnogo vyrozhdeniya”, Zh. vychisl. matem. i matem. fiz., 31:12 (1991), 1808–1825 | MR | Zbl

[3] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 841–859 | Zbl

[4] Shishkin G. I., “Setochnaya approksimatsiya singulyarno vozmuschennogo kvazilineinogo ellipticheskogo uravneniya, vyrozhdayuschegosya v uravnenie pervogo poryadka”, Dokl. AN SSSR, 317:4 (1991), 845–849 | MR

[5] Dulan E., Miller Dzh., Shilders U., Ravnomernye chislennye metody resheniya zadach s pogranichnym sloem, Mir, M., 1983 | MR

[6] Ilin A. M., “Raznostnaya skhema dlya differentsialnogo uravneniya s malym parametrom pri starshei proizvodnoi”, Matem. zam., 6:2 (1969), 237–248 | MR | Zbl

[7] Shishkin G. I., “Grid approximation of singularly perturbed boundary value problem for quasi-linear parabolic equations in the case of complete degeneracy in spatial variables”, Sovet. J. Numer. Analys. Math. Modelling., 6:3 (1991), 243–261 | DOI | MR | Zbl

[8] Fischer R. A., “The wave of advance of advantageous genes”, Ann. Eugenics., 7 (1973), 355–369 | DOI | Zbl

[9] Kolmogorov A. N., Petrovskii I. G., Piskunov N. S., “Issledovanie uravnenii diffuzii, soedinennoi s vozrastaniem kolichestva veschestva, i ego primenenie k odnoi biologicheskoi probleme”, Byull. MGU. Sekts. A, 1937, no. 6, 1–26 | MR

[10] Marri Dzh., Nelineinye differentsialnye uravneniya v biologii. Lektsii o modulyakh, Mir, M., 1983 | Zbl

[11] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[12] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[13] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[14] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1977 | MR

[15] Shishkin G. I., “Approksimatsiya reshenii singulyarno vozmuschennykh kraevykh zadach s parabolicheskim pogranichnym sloem”, Zh. vychisl. matem. i matem. fiz., 29:7 (1989), 963–977 | MR

[16] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989 | MR