A skew-symmetric iterative method for solving a steady convection–diffusion–reaction equation with an indefinite reaction coefficient

详细

An iterative product-type triangular skew-symmetric method (PTSM) is used to solve systems of linear algebraic equations (SLAEs) obtained by approximation with a central-difference scheme of a first-type boundary value problem for convection–diffusion–reaction and standard grid ordering. Sufficient conditions for non-negative definiteness of the SLAE matrix resulting from this approximation are obtained for the indefinite reaction coefficient. This property provides convergence of a wide class of iterative methods (in particular, the PTSM). In test problems, agreement of the theory with computational experiments is shown, and a comparison of the PTSM and SSOR is done.