Numerical Analysis and Applications

, Volume 9, Issue 1, pp 57–65 | Cite as

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



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.


convection–diffusion–reaction equation indefinite reaction coefficient central difference scheme iterative method 


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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Southern Federal UniversityVorovich Institute of Mathematics, Mechanics, and Computer SciencesRostov-on-DonRussia
  2. 2.School of Mathematics and StatisticsLanzhou UniversityLanzhouP.R. China

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