A broad class of methods for the numerical solution of certain classes of partial differential equations. In its simplest form, after a suitable finite-difference replacement of the problem, a system of linear algebraic equations is obtained, perhaps involving thousands of unknowns. These equations are solved iteratively by a process that involves the solution of smaller linear systems arising from a sequence of coarser meshes (see finite-difference method). The method of successive over-relaxation has an important role in the solution of these subsystems. See iterative methods.