The paper presents difference schemes for the solution of axially symmetric problems on equilibrium forms of the free surface of a magnetic fluid subject to a strong magnetic field entailing the large curvature gradients on this surface. The author constructs adaptive grids describing adequately large local deformations of the free surface. The nodes of the nonuniform grid are chosen in such a manner that the principal part of the error of approximation of the difference scheme is minimized. Two methods – a priori, based on the information on the surface shape, and a posteriori, without that, – are developed for determination of an adaptive grid. The proposed techniques are used for the numerical solution of the problem of equilibrium of a drop of a magnetic fluid in strong uniform magnetic field. As a result, peak-shaped structures of the free surface are found.