Using the skew-symmetric part of the coefficient matrix to find an iterative solution of the strongly nonsymmetric positive real linear system of equations

New triangular iterative methods of solving nonsymmetric linear systems of equations with positive real coefficient matrices are proposed. The triangular operator of these iterative methods use the skew-symmetric part of the initial matrix. The convergence analysis and technique for choosing the optimal parameter for the new methods are presented. Several numerical experiments include the solutions of the strongly nonsymmetric linear systems arising from a central finite-difference approximation of the steady convection-diffusion equation with the Peclet numbers $Pe=10^3,10^4$ and $10^5$ . The relative performance of these methods were tested and compared to the popular SOR procedure.