Geodesic
Numerical algorithm for equations of diffusion type on base of multigrid methods
Matematičeskoe modelirovanie, Tome 19 (2007) no. 4, pp. 71-89.

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The new efficient algorithm for solving of parabolic type equations on base of multigrid method is pro-posed, which conserves the advantages of implicit scheme – stability and accuracy, but permits essentially reduce the number of arithmetical operations on each time level. The absolute stability of proposed method is proved on example of one dimensional model problem, the approximation error is investigated and the estimate of solution error is obtained. The calculations of D and 2D model problems showed the good accuracy of proposed method. 
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M. E. Ladonkina; O. Yu. Milyukova; V. F. Tishkin. Numerical algorithm for equations of diffusion type on base of multigrid methods. Matematičeskoe modelirovanie, Tome 19 (2007) no. 4, pp. 71-89. http://geodesic.mathdoc.fr/item/MM_2007_19_4_a6/

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

[2] N. S. Bakhvalov, N. P. Zhidkov, G. M. Kobelkov, Chislennye metody, Nauka, M., 1987 | MR | Zbl

[3] R. P. Fedorenko, “Relaksatsionnyi metod resheniya raznostnykh ellipticheskikh uravnenii”, Zhurn. vychisl. matem. i matem. fiz., 1:5 (1961), 922–927 | MR | Zbl

[4] S. K. Godunov, V. S. Ryabenkii, Raznostnye skhemy, Nauka, M., 1977 | MR

[5] R. Rikhtmaier, K. Morton, Raznostnye metody resheniya kraevykh zadach, Mir, M., 1972

[6] A. A. Samarskii, E. S. Nikolaev, Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[7] V. V. Voevodin, Lineinaya algebra, Nauka, M., 1974 | MR | Zbl