642 Econmnical Difference Schemes for Multidimensional ProblemsvVith regard to yj+i = Y(p) we obtain the syste1n of equations
(E-crPT^2 A~o:)Y(o:) = Fo:,where the right-hand side F o: is expressed in terms of the vectors Y(;3)>
f3 < CY. Such a system can be solved successively moving fro1n CY to CY+ 1
and from s to s + 1 during the course of the elimination. By interchanging
the positions of A;, and At we arrive at the second sche1ne(92)In this case the syste1n can be solved successively moving from CY+ 1 to CY
and from s + 1 to s. Alternation of sche1nes (91) and (92) leads to the third
scheme, which interests us.
By 1neans of the energy 1nethod the reader can derive on his/her own
an a priori estimate for the error z = y-u by exactly the saine reasoning as
before with further reference to the property of summarized approximation.
On this basis the convergence of additive schen1es can be obtained through
such an analysis.