1. Metode newton dan Secanta. 2x3+ 4x2- 2x-5

Metode newton

iterasi Xr f(x) f'(x) xr+1

1 4 179 1262.57936

5

22.57936

550.7754

458.5536

71.71220

4

31.71220

413.3413

1 29.28751.25667

5

41.25667

52.77274

217.5287

91.09849

3

51.09849

30.28083

514.0280

61.07847

3

61.07847

30.00422

913.6064

21.07816

3

71.07816

31.01E-

0613.5999

11.07816

3

Metode secant

Iterasi x1 x2 f(x1) f(x2) x3 f(x3)1 1 3 -1 79 1.025 -0.693722 1.025 3 -0.69372 79 1.042192 -0.475743 1.042192 3 -0.47574 79 1.053911 -0.323684 1.053911 3 -0.32368 79 1.061853 -0.219045 1.061853 3 -0.21904 79 1.067212 -0.147686 1.067212 3 -0.14768 79 1.070818 -0.099327 1.070818 3 -0.09932 79 1.07324 -0.066698 1.07324 3 -0.06669 79 1.074865 -0.044739 1.074865 3 -0.04473 79 1.075955 -0.02998

10 1.075955 3 -0.02998 79 1.076685 -0.0200811 1.076685 3 -0.02008 79 1.077173 -0.0134412 1.077173 3 -0.01344 79 1.0775 -0.00913 1.0775 3 -0.009 79 1.077719 -0.0060214 1.077719 3 -0.00602 79 1.077866 -0.0040315 1.077866 3 -0.00403 79 1.077964 -0.002716 1.077964 3 -0.0027 79 1.07803 -0.0018117 1.07803 3 -0.00181 79 1.078074 -0.0012118 1.078074 3 -0.00121 79 1.078103 -0.0008119 1.078103 3 -0.00081 79 1.078123 -0.0005420 1.078123 3 -0.00054 79 1.078136 -0.0003621 1.078136 3 -0.00036 79 1.078145 -0.0002422 1.078145 3 -0.00024 79 1.078151 -0.0001623 1.078151 3 -0.00016 79 1.078155 -0.0001124 1.078155 3 -0.00011 79 1.078157 -7.3E-0525 1.078157 3 -7.3E-05 79 1.078159 -4.9E-0526 1.078159 3 -4.9E-05 79 1.07816 -3.3E-0527 1.07816 3 -3.3E-05 79 1.078161 -2.2E-0528 1.078161 3 -2.2E-05 79 1.078162 -1.5E-0529 1.078162 3 -1.5E-05 79 1.078162 -9.7E-06

b. ex- 3x2 =0

Metode newton

iterasi Xr f(x) f'(x) xr+11 2 -4.6559 -4.6559 12 1 -0.29 -3.29 0.9118543 0.911854 -0.01242 -2.98911 0.90774 0.9077 9.49E-07 -2.97444 0.9077015 0.907701 -2.4E-09 -2.97444 0.9077016 0.907701 6.1E-12 -2.97444 0.9077017 0.907701 -1.6E-14 -2.97444 0.907701

ketika f(x3) menuju =0 maka x3 merupakan akar dari persamaan

Metode secantIterasi x1 x2 f(x1) f(x2) x3 f(x3)

1 2 4 -4.6559 5.935805 2.87916 -7.225062 2.87916 4 -7.22506 5.935805 3.494479 -4.050323 3.494479 4 -4.05032 5.935805 3.699516 -1.085334 3.699516 4 -1.08533 5.935805 3.745965 -0.228225 3.745965 4 -0.22822 5.935805 3.755371 -0.045446 3.755371 4 -0.04544 5.935805 3.757229 -0.008957 3.757229 4 -0.00895 5.935805 3.757595 -0.001768 3.757595 4 -0.00176 5.935805 3.757666 -0.000359 3.757666 4 -0.00035 5.935805 3.75768 -6.8E-05

10 3.75768 4 -6.8E-05 5.935805 3.757683 -1.3E-0511 3.757683 4 -1.3E-05 5.935805 3.757684 -2.6E-0612 3.757684 4 -2.6E-06 5.935805 3.757684 -5.1E-0713 3.757684 4 -5.1E-07 5.935805 3.757684 -1E-07

c. tan x – x – 1

Metode newton

iterasi Xr f(x) f'(x) xr+11 1 -0.44259 2.425519 1.1824732 1.182473 0.261941 5.97516 1.1386353 1.138635 0.029436 4.70053 1.1323734 1.132373 0.000478 4.549051 1.1322685 1.132268 1.3E-07 4.546566 1.1322686 1.132268 9.33E-15 4.546566 1.1322687 1.132268 0 4.546566 1.132268

Metode secant

Iterasi x1 x2 f(x1) f(x2) x3 f(x3)1 1 1.4 -0.44259 3.397884 1.046098 -0.318442 1.046098 1.4 -0.31844 3.397884 1.076422 -0.22123 1.076422 1.4 -0.2212 3.397884 1.0962 -0.149774 1.0962 1.4 -0.14977 3.397884 1.109025 -0.099615 1.109025 1.4 -0.09961 3.397884 1.117312 -0.065446 1.117312 1.4 -0.06544 3.397884 1.122654 -0.042647 1.122654 1.4 -0.04264 3.397884 1.126091 -0.027648 1.126091 1.4 -0.02764 3.397884 1.128301 -0.017859 1.128301 1.4 -0.01785 3.397884 1.129721 -0.0115

10 1.129721 1.4 -0.0115 3.397884 1.130633 -0.007411 1.130633 1.4 -0.0074 3.397884 1.131218 -0.0047612 1.131218 1.4 -0.00476 3.397884 1.131594 -0.0030613 1.131594 1.4 -0.00306 3.397884 1.131835 -0.0019614 1.131835 1.4 -0.00196 3.397884 1.13199 -0.0012615 1.13199 1.4 -0.00126 3.397884 1.13209 -0.0008116 1.13209 1.4 -0.00081 3.397884 1.132153 -0.0005217 1.132153 1.4 -0.00052 3.397884 1.132194 -0.0003318 1.132194 1.4 -0.00033 3.397884 1.132221 -0.0002119 1.132221 1.4 -0.00021 3.397884 1.132238 -0.0001420 1.132238 1.4 -0.00014 3.397884 1.132248 -8.8E-0521 1.132248 1.4 -8.8E-05 3.397884 1.132255 -5.7E-0522 1.132255 1.4 -5.7E-05 3.397884 1.13226 -3.6E-0523 1.13226 1.4 -3.6E-05 3.397884 1.132263 -2.3E-0524 1.132263 1.4 -2.3E-05 3.397884 1.132264 -1.5E-0525 1.132264 1.4 -1.5E-05 3.397884 1.132266 -9.6E-0626 1.132266 1.4 -9.6E-06 3.397884 1.132266 -6.2E-0627 1.132266 1.4 -6.2E-06 3.397884 1.132267 -4E-0628 1.132267 1.4 -4E-06 3.397884 1.132267 -2.5E-06

2. metode polynomial

10 REM POLYNOMIAL EQUATIONS

20 REM ********** INPUT DATA ***********

30 INPUT "DEGREE OF POLYNOMIAL"; N

40 DIM A(N), B(N): PRINT

50 FOR R = 0 TO N

60 PRINT "A("; R; ")="; : INPUT A (R )

70 NEXT R

80 PRINT : INPUT "NUMBER OF REAL ROOTS"; M

90 LE91 T X = 0: LET Q = 1E-9 : PRINT

100 REM ********** MAIN LOOP *************

110 FOR S = 1 TO M

200 REM ********** DEAL WITH N=1 *************

210 IF N = 1 THEN LET X= -A(1) / A(0) : GOTO 530

300 REM ********** EVALUATE F(X) **************

310 LET B(0) = A(0)

320 FOR R = 1 TO N

330 LET B(R) = B(R-1) * X + A(R)

340 NEXT R

400 REM ********** EVALUATE F(X)***********

410 LET C = B(0)

420 FOR R = 1 TO N-1

430 LET C = C * X + B(R)

440 NEXT R

500 REM ********** NEWTON FORMULA ***********

510 LET Y = B(N) / C: LET X=X-Y

520 IF ABS(Y) > Q THEN GOTO 320

530 PRINT “ ROOT NO “; S; “ =“ ; X

600 REM ********** PREPARE FOR NEXT ROOT *************

610 IF S = M THEN GOTO 710

620 LET N = N-1

630 FOR R = 1 TO N: LET A(R) = B(R) : NEXT R

700 REM ********** END OF MAIN LOOP **************

710 NEXT S

b. x4-5x3+9x2-7x+2=0

METODE NUMERIK

Dosen :

Drs.H. Budi Kudwadi, M.T.

Oleh :

Mufqi Fauzi N

1203897

PROGRAM STUDI TEKNIK SIPIL S1JURUSAN PENDIDIKAN TEKNIK SIPIL

FAKULTAS PENDIDIKAN TEKNOLOGI DAN KEJURUANUNIVERSITAS PENDIDIKAN INDONESIA

BANDUNG2013