Convergence acceleration of triangular iterative methods based on the skew-symmetric part of the matrix Original Research Article

The numerical investigation was done on a 2-D convection–diffusion model problem in a unit square with a small parameter (Peclet number) at the higher derivative. Various ways of assigning coefficients for convective terms were considered. Central difference approximation of this equation produces a system of linear algebraic equations with an essential non-symmetric matrix. The calculations were performed with Peclet number equal to 103–105. Triangular and product triangular iterative methods, which have been built up by special way using only the triangular parts of the skew-symmetric component of the matrix, are used to solve such systems. A way to accelerate convergence of these methods for the case when coefficients of convective terms change very quickly is presented. Comparison with GMRES method was produced.