1549301742-The_Theory_of_Difference_Schemes__Samarskii

64 Basic Concepts of the Theory of Difference Schemes

(x,t+r) (x-h,t+r) (x,t+r) (x+h,t+r

(x-h,t) ( x, t) (x+h,t) ( x, t)

a b

(x-h,t+r) (x,t+r) (x+h,t+r)

(x-h,t) ( x, t) (x+h,t)

c

Figure 4.

is reasonable to place V:rx at the moment t + T, that is, on the upper layer,

so that

(21) L(l) hT 1) -- Vt - Vx;x A ·

By a linear combination of (19') and (21) we get a one-parameter family
of difference operators on the six-point pattern shown in Fig. 4.c for (} f- 0
and(} f- l:

(22)

In the estimation of the order of approximation we substitute into the