Special iterative methods for solution of the steady Convection-Diffusion-Reaction equation with dominant convection

Abstract

Iterative methods based on skew-symmetric splitting of initial matrix, arising from central finite-difference approximation of steady convection-diffusion-reaction (CDR) equation in 2-D domain are considered. The property of obtained large sparse nonsymmetric linear system Au = f is investigated. A new class of triangular and product triangular skew-symmetric iterative methods is presented. Sufficient conditions of convergence for iterative methods of solution CDR with variable coefficient of reaction and dominant convection are obtained. The results of numerical experiments for the solution of a two-dimensional CDR equation are presented. The uniform grid, central differences for the first derivatives, natural ordering of points, Peclet numbers Pe = 103, 104, 105, variable coefficient of reaction and different velocity coefficients have been used.