Abstract:
The iterative product, that is, the triangular skew-symmetric method (PTSM) is used to solve linear algebraic equation systems obtained by approximation of a central-difference scheme of the first boundary value problem of convection-diffusion-reaction and standard grid ordering. Sufficient conditions of a non-negative definiteness of the matrix resulting from this approximation have been obtained for a non-stationary sign of the reaction coefficient. This feature ensures the convergence of a sufficiently wide class of iterative methods, in particular, the PTSM. In the test problems, the compliance of the theory with computational experiments is verified, and comparison of the PTSM and the SSOR is made.
Key words:convection-diffusion-reaction equation, alternating sign coefficient of reaction, central difference scheme, iterative method.