## ABSTRACT

One of the serious developments in computational mathematics owes a debt to economical difference methods available for solving partial differential equations of several spatial variables. Recent years have seen the publications of numerous papers on this subject for multiple equations of parabolic, hyperbolic and elliptic types as well as the constructions of various economical schemes. The general stability theory lies in the foundations of the possible theory of economical methods which will be given special investigation throughout the entire chapter. Two classes of admissible economical schemes are of great importance: schemes with a factorized operator on the upper layer and additive schemes generating a summarized approximation in a certain up-agreed sense. These can depend on the range of situations to be considered.