Nonlinear Monotone Smoothing of an Implicit Difference scheme for Parabolic Equation

摘要

For the two-dimensional parabolic equation (turbulent diffusion equation) by means of the method of nonlinear monotone smoothing using the decomposition scheme, we construct the two-layer implicit monotone scheme of the second order. We prove stability of the developed schemes, obtain majorizing estimations for nonlinear difference operators and estimations of a rate of convergence of a difference solution. We have carried out test calculations of modeling of transfer and diffusion in a two-dimensional region.