On the numerical solution of the Orr–Sommerfeld equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 611-615 Cet article a éte moissonné depuis la source Math-Net.Ru

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An iterative method for solving the Orr–Sommerfeld equation is considered. The method is a combination of two iterative methods, namely, the method of inverse iterations and the method of operator splitting.
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L. Álvarez Díaz; V. V. Ditkin. On the numerical solution of the Orr–Sommerfeld equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 4, pp. 611-615. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_4_a11/

[1] Goldshtik M. A., Shtern V. N., Gidrodinamicheskaya ustoichivost i turbulentnost, Nauka, M., 1977

[2] Davey A., “An automatic orthonormalization method for solving stift boundary-value problems”, J. Comput. Phys., 51 (1983), 343–356 | DOI | MR | Zbl

[3] Meyer G. K., “Continuous orthonormalization for boundary value problems”, J. Comput. Phys., 62 (1986), 248–262 | DOI | MR | Zbl

[4] Abramov A. A., Alvares L. M., “Metod resheniya zhestkikh kraevykh zadach, osnovannyi na rasscheplenii operatora”, Zh. vychisl. matem. i matem. fiz., 29:12 (1989), 1800–1810 | MR

[5] Peters G., Wilkinson J. H., “Inverse iteration, ill-conditioned equations and Newton's method”, SIAM Rev., 21:3 (1979), 336–360 | DOI | MR

[6] Ditkin V. V., “Ob iteratsionnom metode resheniya zadachi na sobstvennye znacheniya dlya puchka lineinykh operatorov”, Zh. vychisl. matem. i matem. fiz., 18:6 (1978), 1377–1384 | MR | Zbl

[7] Ditkin V. V., “Ob iterativnom metode resheniya zadachi na sobstvennye znacheniya v sluchae kratnogo spektra”, Zh. vychisl. matem. i matem. fiz., 27:12 (1987), 1771–1779 | MR | Zbl

[8] Ditkin V. V., “Modifitsirovannyi metod Krandalla–Kikuta”, Zh. vychisl. matem i matem. fiz., 16:4 (1976), 838–846 | MR | Zbl

[9] Thomas L. H., “The stability of plane Poiseuille flow”, Phys. Rev., 91 (1953), 780–783 | DOI | MR | Zbl

[10] Orszag S. A., “Accurate solution of the Orr-Sommerfield stability equation”, J. Fluid. Mech., 50:4 (1971), 689–703 | DOI | Zbl

[11] Davey A. A., “A simple numerical method for solving Orr-Sommerfeld problems”, Quart. J. Mech. Appl. Math., 26 (1973), 401–407 | DOI