The following computer program seeks to solve the boundary value problem in Example 8.2 of Jacques and Judd [10, pp.269-270].
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 3
94 IF RND < .5 THEN A(KK) = 1 - RND ELSE A(KK) = 1 + RND
95 NEXT KK
128 FOR I = 1 TO 10000 STEP 1
129 FOR K = 0 TO 3
131 X(K) = A(K)
132 NEXT K
155 FOR IPP = 1 TO FIX(1 + RND * 3)
181 B = FIX(RND * 4)
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
582 X(1) = (2.0625 * X(0) + .0625 * X(0) ^ 3 - .5) / 2
586 FOR J44 = 2 TO 3
611 X(J44) = (2 * X(J44 - 1) - X(J44 - 2) + .0625 * X(J44 - 1) ^ 3 + .125 * X(J44 - 1) * X(J44 - 2)) / (1 + .125 * X(J44 - 1))
613 NEXT J44
811 PNEW = -1.9375 * X(3) + X(2) - .0625 * X(3) ^ 3 - .125 * X(2) * X(3) + .5
999 P = -ABS(PNEW)
1451 IF P <= M THEN 1670
1657 FOR KEW = 0 TO 3
1658 A(KEW) = X(KEW)
1659 NEXT KEW
1661 M = P
1670 NEXT I
1890 IF M < -.1 THEN 1999
1911 PRINT A(0), A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [20]. Copied by hand from the screen, the computer program’s complete output through JJJJ= -31997 is shown below.
.9789106623451404 .788815898287999 .6607672863276792
.5689129958721464 -2.363544147725161D-12 -32000
.978910662345106 .7888158982879604 .6607672863276316
.5689129958720863 -2.444260017910732D-12 -31999
.9789106623462763 .7888158982892726 .660767286329247
.5689129958741218 -2.906248375636467D-13 -31998
.9789106623603372 .788815898305036 .660767286348652
.5689129958985727 -3.31427122074804D-12 -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 [20], the wall-clock time for obtaining the output through JJJJ= -31997 was three seconds, not including "Creating .EXE file..." time.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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