Geodesic
Numerical algorithm of solving 2d anisotropic parabolic equations
Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 50-56 
O. L. Kritskii. Numerical algorithm of solving 2d anisotropic parabolic equations. Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 50-56. http://geodesic.mathdoc.fr/item/MM_2004_16_3_a5/
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     author = {O. L. Kritskii},
     title = {Numerical algorithm of solving 2d anisotropic parabolic equations},
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     pages = {50--56},
     year = {2004},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A modification of implicit 2D «$\alpha$–$\beta$» iterative algorithm is considered. After this method is applied to numerical solving of anisotropic parabolic equation with boundary conditions of third kind. In modification a new factors as time dependence, normal derivative and diffusive matrix took into account. This factors change a structure of well known algorithm significantly. To improve a performance of constructed iterative method the boundary conditions are approximated by the second order finite differential space scheme. Algorithm was written in a matrix form. The convergence and stability of this iterative process are proved.

[1] Ilin V. P., Metody nepolnoi faktorizatsii dlya resheniya algebraicheskikh sistem, Fizmatlit, M., 1995, 288 pp. | MR

[2] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983, 616 pp. | MR

[3] Chetverushkin B. N., Matematicheskoe modelirovanie zadach dinamiki izluchayuschego gaza, Nauka, M., 1985, 216 pp. | Zbl

[4] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978, 591 pp. | MR | Zbl