Jsun Yui Wong
The following computer program seeks to solve the discrete boundary value problem of Gilat and Subramaniam's Example 9.5 [7] but with 16 subintervals. 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 / 16
91 FOR KK = 1 TO 17
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 17
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 17)
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 17 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(17) + X(15) - 4 * X(16) + 3 * X(17))
1111 P = -PNEW
1451 IF P <= M THEN 1670
1657 FOR KEW = 1 TO 17
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)
1912 PRINT A(10), A(11), A(12), A(13), A(14), A(15), A(16), A(17), 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 .9716120489958967 .943192914883399
.9147110522608525 .886134495565142 .8574308003363542
.8285669835011658 .7995094625588926 .7702239935519866
.7406756077003853 .7108285465765025 .6806461956947915
.6500910163867086 .619124475828551 .5877069750860243
.5557977750355228 .5233549200179414 -1.110223024625157D-16
-32000
1 .9716120489958968 .9431929148833992
.9147110522608528 .8861344955651425 .8574308003363548
.8285669835011664 .799509462558893 .7702239935519879
.7406756077003863 .7108285465765036 .6806461956947927
.65009101638671 .6191244758285524 .587706975086026
.5557977750355244 .5233549200179432 -5.551115123125783D-16
-31999
1 .9716120489958967 .943192914883399
.9147110522608525 .886134495565142 .8574308003363542
.8285669835011658 .7995094625588926 .7702239935519866
.7406756077003853 .7108285465765025 .6806461956947915
.6500910163867086 .619124475828551 .5877069750860243
.5557977750355228 .5233549200179414 -1.110223024625157D-16
-31998
1 .9716120489958967 .943192914883399
.9147110522608525 .886134495565142 .8574308003363542
.8285669835011658 .7995094625588926 .7702239935519866
.7406756077003853 .7108285465765025 .6806461956947915
.6500910163867086 .619124475828551 .5877069750860243
.5557977750355228 .5233549200179414 -1.110223024625157D-16
-31997
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.
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 twenty seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[19] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[20] J. Y. Wong. April 27 2016. The Domino Method of Nonlinear Integer/Continuous/Discrete Programming Seeking To
Solve a 19X19 System of Nonlinear Equations, Fourth Edition.
http://myblogsubstance.typepad.com/substance/2016/04/-the-domino-method-of-nonlinear-integercontinuousdiscrete-programming-seeking-to-solve-a-19x19-syste.html.
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