An experimental study of the efficiency of solvers of 2D boundary value problems on subgrids of quasi-structured rectangular grids is carried out. A solver means a solution method and its software implementation. The following three solvers are considered: a direct solver (Buneman's cyclic reduction method) and two iterative ones (the alternative direction method of Peaceman and Rachford and the successive overrelaxation method). Characteristic features of the study are as follows: 1) the subgrids have a small number of nodes, namely 8 X 8, 16 X 16, 32 X 32, and 64 X 64; 2) the efficiency is estimated not only for single calculations, but also for series of calculations; in each of them the problem is repeatedly solved with different boundary conditions on the same subgrid. Based on a series of calculations, a combined method is proposed, and recommendations on using the solvers are given.