1549301742-The_Theory_of_Difference_Schemes__Samarskii

562 Economical Difference Schen1es for Multidimensional Problems

t=tn

-. ait +Lu- h~ -Lif--L?f h; l

at i 2 12 ~ ·

t=t n

arising from the well-established relations

2 au

Lcxll = -L1L21t +Lex at - Lc,f) Ct= 1, 2.

Further stability analysis is connected with the homogeneous bouncl-
o
ary conditions. In preparation for this, we introduce the space H = r2 h of
0
grid functions and refer to the operators Aa y = -Y.c"x", y E r2 h, as sug-
gested before. All this enables us to concentrate on an operator-difference
schen1e

(54) Byt+A'y=if(t), O<t=nr, y(O)=u 0 ,

with the 1ne1nbers