Geodesic
Numerical algorithm of solving 2d anisotropic parabolic equations
Matematičeskoe modelirovanie, Tome 16 (2004) no. 3, pp. 50-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {O. L. Kritskii},
     title = {Numerical algorithm of solving 2d anisotropic parabolic equations},
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     url = {http://geodesic.mathdoc.fr/item/MM_2004_16_3_a5/}
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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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