The skew-symmetric iterative method for solving the convection-diffusion-reaction equation with the alternating-sign reaction coefficient
Lev Abramovich Krukier1, Boris L’vovich Krukier1, Yu-Mei Huang2
1Instityte Mathematic, Mechanic and computer science of I.I. Vorovich, Stachki 200/1, k. 2, Rostov on Done, 344090
2Scool mathematic and statistics, Landjou, China, 730000
Keywords: уравнение конвекции-диффузии-реакции, знакопеременный коэффициент реакции, центрально-разностная схема, итерационные методы, convection-diffusion-reaction equation, alternating sign coefficient of reaction, central difference scheme, iterative method
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.
|
