Discretized elliptic problems are typically solved by a preconditioned Krylov iterative method. For nonsymmetric linear systems there exist several versions of Krylov iterations, but none of them can be considered as the best for all problems. The goal of the project is to code some of these methods and test their performance for various model problems arising from elliptic convection-diffusion PDEs, and study the relation of the results to the coefficients of the PDE.