The following computer program seeks to solve the system of nonlinear equations of the discrete boundary value problem on pp. 402-405 of Gilat and Subramanian [6, Example 9.4]. Also see Gilat and Subramanian [7]. While the preceding paper has five sub-intervals, the present paper has twenty sub-intervals.
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 21
94 A(KK) = 293 + RND * 200
95 NEXT KK
128 FOR I = 1 TO 20000000 STEP 1
129 FOR K = 1 TO 21
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = 1 + FIX(RND * 22)
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(21) = 293
605 FOR J49 = 21 TO 3 STEP -1
610 P(J49) = X(J49 - 2) - (2 + .005 ^ 2 * betaa) * X(J49 - 1) - .005 ^ 2 * betab * X(J49 - 1) ^ 4 + X(J49) + .005 ^ 2 * (betaa * 293 + betab * 293 ^ 4)
612 NEXT J49
660 PS = 0
661 FOR J33 = 21 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 21
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)
1919 PRINT A(21), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [18]. Copied by hand from the screen, the computer program’s complete output through JJJJ= -32000 is shown below.
473 459.455895068255 446.6932249241943
434.6475924043841 423.2590645622598
412.4716933656588 402.2330921869252 392.4940590698486
383.2082393784908 374.331821732474
365.8232621978106 357.6430325441322 349.7533890177581
342.1181586515432 334.7025405843482
327.4729202056817 320.3966942320405 313.442105080995
306.5780831026808 299.7740953874252
293 -2.877462553516411D-08 -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 [18], the wall-clock time for obtaining the output through JJJJ= -32000 was four minutes.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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