1549301742-The_Theory_of_Difference_Schemes__Samarskii

The alternative-triangular method 707

where fia = h and h! differ from h only at the near-boundary nodes, the

intention is to use scheme (81) with the members aa(x) - 1 and fia = h,

so that

YI -Yh = p.

In an attempt to adapt here MATM, the functions v 1 (x) and v 2 (x) are

declared to be solutions of one and the same equation

vi -y" =0, /3=3-cx, et=l,2,

but with different right-hand sides

l

P1(x) = hfi+'

"'

( l

1

p. 2 x) = - -^1 - -l I.

2 h h+ h-

0' "'

Denote by xa = la(xf3) and xa = La(xf3) the endpoints of an interval

~a and by h~ and ht irregular steps at the left and the right ends of this

interval; in so doing

The functions v~a)(x) and v~")(x) can be fonncl in explicit fon11, while the

functions <f!a(xf3) and 1/Ja(xf3) are expressed by

__ l_ (Leo,(xp) - la(i·f3))2

<f!a(xp) - 2 h2 2 + 1'

1

1/Ju(xf3)=2, ,8=3-n, ct=l,2,

giving ~ due to (88) and evaluating the number of the iterations:

(91)

In (2/c)

n 0 (c) - ---'----==

• 3.4 ,;r;rr;'

where! 0 is the diameter of the domain G of interest.