Extending the computational process of the preceding paper

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below seeks to solve simultaneously the following nonlinear system of equations in Jorge Donis del Alamo [44]:

(4.5 * 10 ^ -4) * X(2) = X(3) * X(4))

X(4) = (10 ^ -14) / X(1)

X(3) = .02 - X(2)

X(4) = X(1) + X(3).

One notes line 222 through line 476, which are 222 X(1) = (10 ^ -14) / X(4), 225 X(3) = X(4) - X(1), 229 X(2) = .02 - X(3), and 476 PD1 = -ABS((4.5 * 10 ^ -4) * X(2) - X(3) * X(4)).

0 DEFDBL A-Z

1 REM DEFINT I, J, K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -3D+30

115 FOR J44 = 1 TO 4

116 A(J44) = -5 + RND * 10

122 NEXT J44

128 FOR i = 1 TO 50000

129 FOR KKQQ = 1 TO 4

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 4)

140 B = 1 + FIX(RND * 4)

144 IF RND < .5 THEN 160 ELSE GOTO 167

160 r = (1 - RND * 2) * A(B)

164 X(B) = A(B) + (RND ^ (RND * 15)) * r

165 GOTO 168

167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)

168 NEXT IPP

222 X(1) = (10 ^ -14) / X(4)

225 X(3) = X(4) - X(1)

229 X(2) = .02 - X(3)

476 PD1 = -ABS((4.5 * 10 ^ -4) * X(2) - X(3) * X(4))

479 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 4

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1670 NEXT i

1779 REM IF M < -.00001 THEN 1999

1904 PRINT A(1), A(2), A(3), A(4), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102]--GW-BASIC, among others, can also handle this computer program--its complete output of one run through JJJJ= -31998 is shown below:

**-3.09269518532017D-12 2.323342566635774D-02 -3.233425666357738D-02 ****-3.233425669450433D-03 -1.232499112704011D-22 -32000**

**-3.09269518532017D-12 2.323342566635774D-02 -3.233425666357738D-02 ****-3.233425669450433D-03 -1.232499112704011D-22 -31999**

**3.592695184196558D-12 1.721657433364226D-02 2.783425666357738D-03 ****2.783425669950433D-03 -3.010937429693021D-22 -31998**

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM, 64-bit Operating System, and QB64v1000-win [102], the wall-clock time (**not CPU** **time**) for obtaining the output through JJJJ = -31998 was 3 seconds, counting from "Starting program...". One can compare the computational results above with those in Jorge Donis del Alamo [44].

The computational results presented above were obtained from the following computer system:

Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type: 64-bit Operating System.

**Acknowledgement**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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