Numerical algorithm of solving 2d anisotropic parabolic equations

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.