1549301742-The_Theory_of_Difference_Schemes__Samarskii

Higher-accuracy schemes for Poisson's equation 291

7 ,,._ ____^4 ......., 6

3 <)----------""('+---------~ 1

s^4 5

Figure 16.

We substitute here Lu= -f and replace L 1 L 2 u by the difference operator.

The outcome of this is

This operator is defined on the nine-point pattern shown in Fig. 16.

The expression for A 1 A 2 u such that

is needed in the estimation of the error of approximation to A 1 A 2 u-L 1 L 2 u
by virtue of the well-established expansion

(4)

v(x + h) - 2 v(x) + v(x - h)

Av= vxx = h2

=v"(~), ~=x+Bh, IBl<l,