Jsun Yui Wong
The following computer program seeks to solve the discrete boundary value problem on pp. 402-405 of Gilat and Subramaniam [7, Example 9.4] but with 40 subintervals. Also see Gilat and Subramaniam [8, pp. 486-489, Example 11.4].
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
33 betaa = (40 * .016) / (240 * 1.6D-05)
35 betab = (.4 * 5.67D-08 * .016) / (240 * 1.6D-05)
91 FOR KK = 1 TO 41
94 A(KK) = 293 + RND * 200
95 NEXT KK
128 FOR I = 1 TO 60000000 STEP .5
129 FOR K = 1 TO 41
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 42)
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
566 X(1) = 473
577 X(41) = 293
605 FOR J49 = 41 TO 3 STEP -1
610 P(J49) = X(J49 - 2) - (2 + .0025 ^ 2 * betaa) * X(J49 - 1) - .0025 ^ 2 * betab * X(J49 - 1) ^ 4 + X(J49) + .0025 ^ 2 * (betaa * 293 + betab * 293 ^ 4)
612 NEXT J49
660 PS = 0
661 FOR J33 = 41 TO 3 STEP -1
663 PS = PS + ABS(P(J33))
668 NEXT J33
1111 P = -PS
1451 IF P <= M THEN 1670
1657 FOR KEW = 1 TO 41
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)
1912 PRINT A(6), A(7), A(8), A(9), A(10)
1913 PRINT A(11), A(12), A(13), A(14), A(15)
1914 PRINT A(16), A(17), A(18), A(19), A(20)
1915 PRINT A(21), A(22), A(23), A(24), A(25)
1917 PRINT A(26), A(27), A(28), A(29), A(30)
1919 PRINT A(31), A(32), A(33), A(34), A(35)
1920 PRINT A(36), A(37), A(38), A(39), A(40)
1949 PRINT A(41), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [19]. Copied by hand from the screen, the computer program’s complete output through JJJJ= -32000 is shown below.
473 466.1252645234572 459.454396830037
452.9788859253014 446.6905337719811
440.5814376383047 434.6439736592641 428.8707813666962
423.254749209604 417.7890009312665
412.4668827467266 407.2819512476794 402.2279619476744
397.2988585078405 392.48876246803
387.7919634893053 383.202910101684 378.7162009623876
374.3265763185161 370.0289100762415
365.818202063232 361.6895706072123 357.6382456273334
353.6595616625091 349.7489513643077
345.9019392643605 342.1141356057881 338.3812304285532
334.698987914485 331.0632407750056
327.4698849573408 323.9148742937587 320.394215500285
316.9039631286514 313.4402146999775
309.9991059405026 306.5768061200266 303.1695134443441
299.7734505337667 296.3848599907126
293 -6.084179225805805D-07 -32000
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= -32000 was 33 minutes.
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.
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Solve a 19X19 System of Nonlinear Equations, Fourth Edition.
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