The following computer program seeks to solve the discrete boundary value problem of Gilat and Subramaniam's Example 9.5 [7]. Also see Gilat and Subramaniam [8, Example 11.5].
0 DEFDBL A-Z
3 DEFINT J, K
4 DIM X(32768), A(32768), P(32768), K(32768)
5 FOR JJJJ = -32000 TO 32000
14 RANDOMIZE JJJJ
16 M = -1D+50
55 H = 1 / 8
91 FOR KK = 1 TO 9
94 IF RND < .5 THEN A(KK) = 1 - RND ELSE A(KK) = 1 + RND
95 NEXT KK
128 FOR I = 1 TO 100000 STEP 1
129 FOR K = 1 TO 9
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 9)
183 R = (1 - RND * 2) * A(B)
188 IF RND < .2 THEN X(B) = A(B) + RND * R ELSE IF RND < .25 THEN X(B) = A(B) + RND ^ 3 * R ELSE IF RND < .333 THEN X(B) = A(B) + RND ^ 5 * R ELSE IF RND < .5 THEN X(B) = A(B) + RND ^ 7 * R ELSE X(B) = A(B) + RND ^ 9 * R
199 NEXT IPP
571 X(1) = 1
580 X(3) = ((4 + H ^ 2) * X(2) - 2 - H ^ 2 * EXP(-.2 * H)) / 2
581 FOR J44 = 4 TO 9 STEP 1
582 X(J44) = (-2 * X(J44 - 2) + (4 + H ^ 2) * X(J44 - 1) - H ^ 2 * EXP(-.2 * (J44 - 2) * H)) / 2
584 NEXT J44
610 PNEW = ABS(2 * H * X(9) + X(7) - 4 * X(8) + 3 * X(9))
1111 P = -PNEW
1451 IF P <= M THEN 1670
1657 FOR KEW = 1 TO 9
1658 A(KEW) = X(KEW)
1659 NEXT KEW
1661 M = P
1670 NEXT I
1890 REM IF M < -.1 THEN 1999
1911 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [19]. Copied by hand from the screen, the computer program’s output through JJJJ= -31997 is shown below.
1 .943153486079235 .8860557500807424
.828448844750844 .7700662000336197 .7106306551757421
.649852405260003 .5874268461945267 .5230323013901858
-1.110223024625157D-16 -32000
1 .943153486079235 .8860557500807424
.828448844750844 .7700662000336197 .7106306551757421
.649852405260003 .5874268461945267 .5230323013901858
-1.110223024625157D-16 -31999
1 .943153486079235 .8860557500807424
.828448844750844 .7700662000336197 .7106306551757421
.649852405260003 .5874268461945267 .5230323013901858
-1.110223024625157D-16 -31998
1 .943153486079235 .8860557500807424
.828448844750844 .7700662000336197 .7106306551757421
.649852405260003 .5874268461945267 .5230323013901858
-1.110223024625157D-16 -31997
Above there is no rounding by hand; it is just straight copying by hand from the screen.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and with qb64v1000-win [19], the wall-clock time for obtaining the output through JJJJ= -31997 was fifteen seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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