A high performance iterative algorithm of solving 2D parabolic equations

In this paper 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 the third kind. In modifying 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 the performance of a constructed iterative method the boundary conditions are approximated by the second order finite differential space scheme. The algorithm was written in a matrix form. The convergence and stability of this iterative process are proven