Jsun Yui Wong
The following computer program seeks to solve the discrete boundary value problem on pp. 634-635 of Chapra but with 60 subintervals [4, Example 24.7, http://www.learngroup.org/uploads/2014-10-27/Applied_Num_Methods_with_MATLAB_for_Engineers_3ed1.pdf].
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
91 FOR KK = 0 TO 60
94 A(KK) = 300 + RND * 100
95 NEXT KK
128 FOR I = 1 TO 90000000 STEP .5
129 FOR K = 0 TO 60
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 60)
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(0) = 300
577 X(60) = 400
581 FOR J49 = 60 TO 2 STEP -1
584 P(J49) = -X(J49 - 2) + (2 + .05 * (1 / 6) ^ 2) * X(J49 - 1) - X(J49) - .05 * (1 / 6) ^ 2 * 200 - 2.7D-09 * (1 / 6) ^ 2 * (200 ^ 4 - X(J49 - 1) ^ 4)
588 NEXT J49
660 PS = 0
661 FOR J33 = 60 TO 2 STEP -1
663 PS = PS + ABS(P(J33))
668 NEXT J33
1111 P = -PS
1451 IF P <= M THEN 1670
1657 FOR KEW = 0 TO 60
1658 A(KEW) = X(KEW)
1659 NEXT KEW
1661 M = P
1670 NEXT I
1890 REM IF M < -.1 THEN 1999
1911 PRINT A(0), A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), A(10), A(11), A(12), A(13), A(14), A(15), A(16), A(17), A(18), A(19), A(20), A(21), A(22), A(23), A(24), A(25), A(26), A(27), A(28), A(29), A(30), A(31), A(32), A(33)
1918 PRINT A(34), A(35), A(36), A(37), A(38), A(39)
1919 PRINT A(40), A(41), A(42), A(43), A(44)
1920 PRINT A(45), A(46), A(47), A(48), A(49)
1921 PRINT A(50), A(51), A(52), A(53), A(54)
1922 PRINT A(55), A(56), A(57), A(58), A(59)
1929 PRINT A(60), 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= -32000 is summarized below.
300 293.3486033725414 287.2622466954858
281.687798890065 276.5790144331143 271.8954620096952
.
.
.
333.638096933311 344.2675350499851 356.0308714326258
369.095986296642 383.6678904090441
400 -3.66678468084492D-07 -32000
Above there is no rounding by hand; it is just straight copying by hand from the screen.
Only twelve of the 61 A's of line 1911 through line 1929 are shown above.
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 one hour and fifteen 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.
[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.
[21] M. Ziani, F. Guyomarc’h, An Autoadaptive Limited Memory Broyden’s Method To Solve Systems of Nonlinear Equations, Applied Mathematics and Computation 205 (2008) pp. 202-211. web.info.uvt.ro/~cristiana.drogoescu/MC/broyden.pdf.
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