The solution of convection-di usion problems is a challenging task for numerical methods owing to the fact that the governing equation includes the di usion component and drift or convection component. In case when the coecients of these terms are comparable, the problem can be solved numerically using a traditional nite-di erence approximation. However, in many applications the ratio between the convection and the di usion coecients is very large. In this case, the solution has an exponential character and standard approaches to the construction of di erence schemes lead to the numerical solutions with high error on coarse grids. We consider several diverse approaches for construction the nite-di erence schemes and carry out a comparative analysis of the e ectiveness of obtained schemes by solving a speci c problem.