Geodesic
Enhancement of SSOR method efficiency on the base of improved spectral estimations
Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 20-32.

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The work is dedicated to building of modified SSOR method for finite-difference scheme of three-dimensional elliptical equations with linear source function that takes $n_0(\varepsilon)\cong O\left(1/\root4\of{||h||}\right)$ iterations in case of special limitation on source function is built. In the article $\gamma_1$ parameter estimation was improved by the instrumentality of separate analysis of diagonal component of the matrix, which allows to decrease the amount of iterations twice. Calculations and results of numerical experiments for Dirichlet problem of Poisson equation and Poisson equation with linear source function of $q(x)u(x)$ kind and nonstationary heat equation are given in this paper.
Keywords: numerical methods, iteration method, modified SSOR
Mots-clés : Poisson equation. 
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A. I. Sukhinov; A. V. Shishenya. Enhancement of SSOR method efficiency on the base of improved spectral estimations. Matematičeskoe modelirovanie, Tome 24 (2012) no. 11, pp. 20-32. http://geodesic.mathdoc.fr/item/MM_2012_24_11_a1/

[1] Konovalov A. N., “Optimalnye adaptivnye predobuslovlivateli v staticheskikh zadachakh lineinoi teorii uprugosti”, Differentsialnye uravneniya, 45:7 (2009), 1023–1030 | MR

[2] Kucherov A. B., Nikolaev E. S., “Poperemenno-treugolnyi iteratsionnyi metod resheniya setochnykh ellipticheskikh uravneniya v pryamougolnike”, Zh. vychisl. matem. i matem. fiz., 16:5 (1976), 1164–1174 | MR | Zbl

[3] Sukhinov A. I., “Modifitsirovannyi poperemenno-treugolnyi metod dlya zadach teploprovodnosti i filtratsii”, Vychislitelnye sistemy i algoritmy, Rostovskii gos. universitet, Rostov-na-Donu, 1984, 52–57

[4] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya obratnykh zadach konvektsii-diffuzii, Editorial URSS, M., 2004, 248 pp.

[5] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978, 592 pp. | MR