ABSTRACT
Difference methods are usually understood as particular cases of grid methods that, at some stages, approximate derivatives by difference quotients. This chapter shows that the strengthened variant of the Kolmogorov-Bakhvalov hypothesis can be proved for difference methods. It discusses briefly certain difference approximations for fourth-order elliptic equations and systems, and indicates certain important classes of practical problems that were solved by asymptotically optimal iterative methods. The chapter stresses the role of averaging in construction of difference schemes on general grids. Similar algorithms were constructed and applied for geometric nonlinear problems associated with certain net shells and tires of various structures in the Computer Center of Research Institute of Tire Industry in Moscow.
