A Survey on Generalized Difference Methods and Their Analysis

A survey is given for the generalized difference methods. Included are the main results of the authors and their Chinese colleagues in the recent ten odd years on the generalized difference methods for differential equations, such as the construction of the generalized difference schemes for elliptic, parabolic and hyperbolic equations; the error estimates in Sobolev norms and the superconvergences; and the applications of the generalized difference methods in electromagnetic and fluid computations.