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 Matem. Mod., 2004, Volume 16, Number 3, Pages 50–56 (Mi mm332)

Numerical algorithm of solving 2d anisotropic parabolic equations

O. L. Kritskii

Tomsk Polytechnic University

Abstract: 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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Citation: O. L. Kritskii, “Numerical algorithm of solving 2d anisotropic parabolic equations”, Matem. Mod., 16:3 (2004), 50–56

Citation in format AMSBIB
\Bibitem{Kri04} \by O.~L.~Kritskii \paper Numerical algorithm of solving 2d anisotropic parabolic equations \jour Matem. Mod. \yr 2004 \vol 16 \issue 3 \pages 50--56 \mathnet{http://mi.mathnet.ru/mm332} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2061746} \zmath{https://zbmath.org/?q=an:1047.65077}