A very general computer program for solving simultaneously nonlinear/linear systems of equations: another illustration

Jsun Yui Wong

Similar to the computer programs of the preceding papers, the computer program listed below seeks to solve the following system of of nonlinear equations from Sharma and Gupta [79, p. 8, Problem 1]:

X(1) + e ^ X(2) - COS(X(2))

3 * X(1) - X(2) - SIN(X(2)).

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 2

116 A(J44) = -1 + RND * 2

122 NEXT J44

128 FOR i = 1 TO 70000

129 FOR KKQQ = 1 TO 2

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 2)

140 B = 1 + FIX(RND * 2)

144 IF RND < .5 THEN 160 ELSE GOTO 167

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

164 X(B) = A(B) + (RND ^ (RND * 13)) * 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

221 REM J45 = 1 + FIX(RND * 15)

224 REM IF RND < .5 THEN X(J45) = A(J45) - RND * .01 * A(J45) ELSE X(J45) = A(J45) + RND * .01 * A(J45)

333 FOR J44 = 1 TO 2

334 REM IF X(J44) < -10 THEN 1670

335 IF X(J44) < 0 THEN 1670

336 IF X(J44) > 1 THEN 1670

338 NEXT J44

340 REM SUMOF13 = X(1) + X(2) + X(3) + X(4) + X(5) + X(6) + X(7) + X(8) + X(9) + X(10) + X(11) + X(12) + X(13)

343 REM FOR J44 = 1 TO 13

351 LHS(1) = X(1) + 2.718281828 ^ X(2) - COS(X(2))

352 LHS(2) = 3 * X(1) - X(2) - SIN(X(2))

353 REM LHS(3) = 12 * X(3) + SIN(X(3)) - 1

377 REM NEXT J44

464 PD1 = -ABS(LHS(1) - 0) - ABS(LHS(2) - 0)

466 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 2

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1670 NEXT i

1777 IF M < -.000001 THEN 1999

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

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31999 is shown below:

1.785791033462545D-13 2.678685098552974D-13 -4.463652405382785D-13

-32000**2.829662332959287D-17 7.244493481874815D-17 -4.824699668432263D-17****-31999**

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By unot sing the following computer system and QB64v1000-win [102], the wall-clock time (**CPU time**) for obtaining the output through JJJJ = -31999 was 1 second, counting from "Starting program...".

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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