1549301742-The_Theory_of_Difference_Schemes__Samarskii

The alternating direction niethod 557

with further reference to the following asymptotic relations:

As a final result we obtain

thereby justifying that scheme (33)-(34) generates a second-order approx-

i1nation:

Further developn1ent of s01ne a priori estin1ate for a solution of the
problem concerned is mostly based on an operator-difference analog of prob-
lem (37)-(38) such as

(39)

zn+l - z

0.5 T + A l ( in+l/2 ) Z -+ A 2 ( in+l ) Z n+l =^0 'f/2 /,'11 '

n=0,1,2,. .. , z(O)=O,

where A 1 (t) and A 2 (t) are linear operators in a Hilbert space H:

At : H c--H,