1

INSTITUTO TECNOLÓGICO DE MATEHUALA

Equipo # 1

09660007 Carrizalez Cisneros Hugo René

09660022 Licea Morales José Alberto

09660026 Martínez Silva José Isaac

09660035 Orozco López Iván Guadalupe

09660058 Vázquez Torres Jonathan Cruz

MÉTODOS NUMÉRICOS Título del Trabajo

Carrera: Ingeniería Civil Semestre: Quinto Docente: Ing. Martín Luis Ledezma Hernández

Periodo: Agosto-Diciembre 2011

Matehuala, S.L.P. 30 de Octubre 2011

2

Resuelva el poblema propuesto, genere y publique un documento en pdf con la solución del problema y la siguiente estructura: Portada -Enunciado -Grafica de solución -Código Matlab método de punto fijo -Resultados punto fijo -Código Matlab método de Newton-Raphson -Resultados Newton-Raphson

3

GRAFICA RAIZ NEGATIVA: x=-2:0.001:3; y=-0.9*x.^2+1.7*x+2.5; plot(x,y), grid, title('y=-0.9*x.^2+1.7*x+2.5');

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3-5

-4

-3

-2

-1

0

1

2

3

4

X: -0.975

Y: -0.01306

y=-0.9*x.2+1.7*x+2.5

PUNTO FIJO:

clc; et=0; ea=100; es=0.01; vv=-0.975; x=-1; i=0; disp (' i x et ea') while es < ea, et=((vv-x)/vv)*100; if i~=0; ea=abs((x-xa)/x)*100; end xa=x; fprintf('%2.0f %9.8f %5.4f %4.5f\n ' , i,x,et,ea); x=-(sqrt((1.7*x+2.5)/0.9)); i=i+1; end

RESULTADOS:

i x et ea

0 -1.00000000 -2.5641 100.00000

1 -0.94280904 3.3016 6.06602

2 -0.99845694 -2.4058 5.57339

3 -0.94435352 3.1432 5.72915

4 -0.99699494 -2.2559 5.28001

5 -0.94581452 2.9934 5.41125

6 -0.99560998 -2.1138 5.00150

7 -0.94719647 2.8516 5.11124

8 -0.99429819 -1.9793 4.73718

9 -0.94850354 2.7176 4.82810

10 -0.99305588 -1.8519 4.48639

11 -0.94973973 2.5908 4.56084

12 -0.99187950 -1.7312 4.24848

13 -0.95090883 2.4709 4.30858

14 -0.99076569 -1.6170 4.02283

15 -0.95201443 2.3575 4.07045

16 -0.98971122 -1.5088 3.80887

17 -0.95305994 2.2503 3.84564

18 -0.98871302 -1.4065 3.60601

19 -0.95404860 2.1489 3.63340

20 -0.98776818 -1.3096 3.41371

4

21 -0.95498348 2.0530 3.43301

22 -0.98687390 -1.2178 3.23146

23 -0.95586747 1.9623 3.24380

24 -0.98602755 -1.1310 3.05875

25 -0.95670335 1.8766 3.06513

26 -0.98522660 -1.0489 2.89510

27 -0.95749371 1.7955 2.89640

28 -0.98446867 -0.9711 2.74005

29 -0.95824102 1.7189 2.73706

30 -0.98375147 -0.8976 2.59318

31 -0.95894763 1.6464 2.58657

32 -0.98307287 -0.8280 2.45406

33 -0.95961574 1.5779 2.44443

34 -0.98243080 -0.7621 2.32231

35 -0.96024745 1.5131 2.31017

36 -0.98182333 -0.6998 2.19753

37 -0.96084474 1.4518 2.18335

38 -0.98124861 -0.6409 2.07938

39 -0.96140948 1.3939 2.06355

40 -0.98070490 -0.5851 1.96751

41 -0.96194344 1.3391 1.95037

42 -0.98019054 -0.5324 1.86159

43 -0.96244831 1.2874 1.84345

44 -0.97970396 -0.4825 1.76131

45 -0.96292567 1.2384 1.74243

46 -0.97924367 -0.4352 1.66639

47 -0.96337702 1.1921 1.64698

48 -0.97880827 -0.3906 1.57653

49 -0.96380377 1.1483 1.55680

50 -0.97839641 -0.3483 1.49149

51 -0.96420727 1.1069 1.47159

52 -0.97800684 -0.3084 1.41099

53 -0.96458879 1.0678 1.39106

54 -0.97763834 -0.2706 1.33480

55 -0.96494952 1.0308 1.31497

56 -0.97728980 -0.2349 1.26270

57 -0.96529059 0.9958 1.24307

58 -0.97696013 -0.2010 1.19447

59 -0.96561309 0.9628 1.17511

60 -0.97664832 -0.1691 1.12991

61 -0.96591802 0.9315 1.11089

62 -0.97635340 -0.1388 1.06881

63 -0.96620634 0.9019 1.05020

64 -0.97607447 -0.1102 1.01100

65 -0.96647895 0.8740 0.99283

66 -0.97581065 -0.0831 0.95630

67 -0.96673672 0.8475 0.93861

68 -0.97556114 -0.0576 0.90455

69 -0.96698045 0.8225 0.88737

70 -0.97532515 -0.0333 0.85558

71 -0.96721090 0.7989 0.83893

72 -0.97510197 -0.0105 0.80926

73 -0.96742881 0.7765 0.79315

74 -0.97489089 0.0112 0.76543

75 -0.96763485 0.7554 0.74987

76 -0.97469126 0.0317 0.72396

77 -0.96782968 0.7354 0.70897

78 -0.97450247 0.0510 0.68474

79 -0.96801389 0.7165 0.67030

80 -0.97432391 0.0693 0.64763

81 -0.96818808 0.6987 0.63374

82 -0.97415505 0.0867 0.61253

83 -0.96835279 0.6818 0.59919

84 -0.97399536 0.1030 0.57932

85 -0.96850853 0.6658 0.56652

86 -0.97384433 0.1185 0.54791

87 -0.96865579 0.6507 0.53564

88 -0.97370150 0.1332 0.51820

89 -0.96879504 0.6364 0.50645

90 -0.97356643 0.1470 0.49009

91 -0.96892671 0.6229 0.47885

92 -0.97343869 0.1601 0.46351

93 -0.96905121 0.6101 0.45276

94 -0.97331789 0.1725 0.43836

95 -0.96916894 0.5981 0.42809

96 -0.97320364 0.1842 0.41458

97 -0.96928026 0.5866 0.40477

98 -0.97309561 0.1953 0.39208

99 -0.96938553 0.5758 0.38273

100 -0.97299344 0.2058 0.37081

101 -0.96948506 0.5656 0.36188

102 -0.97289682 0.2157 0.35068

103 -0.96957918 0.5560 0.34217

104 -0.97280545 0.2251 0.33165

105 -0.96966818 0.5469 0.32354

106 -0.97271904 0.2339 0.31364

107 -0.96975234 0.5382 0.30592

108 -0.97263732 0.2423 0.29661

109 -0.96983192 0.5301 0.28927

110 -0.97256005 0.2503 0.28051

111 -0.96990717 0.5223 0.27352

112 -0.97248697 0.2577 0.26528

113 -0.96997832 0.5150 0.25863

114 -0.97241787 0.2648 0.25087

115 -0.97004561 0.5081 0.24455

116 -0.97235251 0.2715 0.23725

117 -0.97010923 0.5016 0.23124

118 -0.97229071 0.2779 0.22437

119 -0.97016939 0.4954 0.21865

120 -0.97223227 0.2839 0.21218

121 -0.97022628 0.4896 0.20675

122 -0.97217701 0.2895 0.20066

5

72 -0.97510197 -0.0105 0.80926

73 -0.96742881 0.7765 0.79315

74 -0.97489089 0.0112 0.76543

75 -0.96763485 0.7554 0.74987

76 -0.97469126 0.0317 0.72396

77 -0.96782968 0.7354 0.70897

78 -0.97450247 0.0510 0.68474

79 -0.96801389 0.7165 0.67030

80 -0.97432391 0.0693 0.64763

81 -0.96818808 0.6987 0.63374

82 -0.97415505 0.0867 0.61253

83 -0.96835279 0.6818 0.59919

84 -0.97399536 0.1030 0.57932

85 -0.96850853 0.6658 0.56652

86 -0.97384433 0.1185 0.54791

87 -0.96865579 0.6507 0.53564

88 -0.97370150 0.1332 0.51820

89 -0.96879504 0.6364 0.50645

90 -0.97356643 0.1470 0.49009

91 -0.96892671 0.6229 0.47885

92 -0.97343869 0.1601 0.46351

93 -0.96905121 0.6101 0.45276

94 -0.97331789 0.1725 0.43836

95 -0.96916894 0.5981 0.42809

96 -0.97320364 0.1842 0.41458

97 -0.96928026 0.5866 0.40477

98 -0.97309561 0.1953 0.39208

99 -0.96938553 0.5758 0.38273

100 -0.97299344 0.2058 0.37081

101 -0.96948506 0.5656 0.36188

102 -0.97289682 0.2157 0.35068

103 -0.96957918 0.5560 0.34217

104 -0.97280545 0.2251 0.33165

105 -0.96966818 0.5469 0.32354

106 -0.97271904 0.2339 0.31364

107 -0.96975234 0.5382 0.30592

108 -0.97263732 0.2423 0.29661

109 -0.96983192 0.5301 0.28927

110 -0.97256005 0.2503 0.28051

111 -0.96990717 0.5223 0.27352

112 -0.97248697 0.2577 0.26528

113 -0.96997832 0.5150 0.25863

114 -0.97241787 0.2648 0.25087

115 -0.97004561 0.5081 0.24455

116 -0.97235251 0.2715 0.23725

117 -0.97010923 0.5016 0.23124

118 -0.97229071 0.2779 0.22437

119 -0.97016939 0.4954 0.21865

120 -0.97223227 0.2839 0.21218

121 -0.97022628 0.4896 0.20675

122 -0.97217701 0.2895 0.20066

123 -0.97028008 0.4841 0.19550

124 -0.97212474 0.2949 0.18976

125 -0.97033095 0.4789 0.18486

126 -0.97207532 0.3000 0.17945

127 -0.97037905 0.4739 0.17480

128 -0.97202858 0.3048 0.16970

129 -0.97042454 0.4693 0.16529

130 -0.97198439 0.3093 0.16048

131 -0.97046755 0.4649 0.15630

132 -0.97194259 0.3136 0.15176

133 -0.97050823 0.4607 0.14780

134 -0.97190307 0.3176 0.14352

135 -0.97054669 0.4568 0.13975

136 -0.97186569 0.3215 0.13572

137 -0.97058306 0.4530 0.13215

138 -0.97183035 0.3251 0.12834

139 -0.97061745 0.4495 0.12496

140 -0.97179693 0.3285 0.12137

141 -0.97064997 0.4462 0.11816

142 -0.97176532 0.3318 0.11478

143 -0.97068072 0.4430 0.11174

144 -0.97173543 0.3348 0.10854

145 -0.97070980 0.4400 0.10566

146 -0.97170717 0.3377 0.10264

147 -0.97073730 0.4372 0.09991

148 -0.97168044 0.3405 0.09706

149 -0.97076330 0.4345 0.09448

150 -0.97165517 0.3431 0.09179

151 -0.97078789 0.4320 0.08934

152 -0.97163126 0.3455 0.08680

153 -0.97081114 0.4296 0.08448

154 -0.97160866 0.3478 0.08208

155 -0.97083313 0.4274 0.07988

156 -0.97158729 0.3500 0.07762

157 -0.97085392 0.4252 0.07554

158 -0.97156708 0.3521 0.07340

159 -0.97087358 0.4232 0.07143

160 -0.97154797 0.3541 0.06941

161 -0.97089218 0.4213 0.06755

162 -0.97152989 0.3559 0.06564

163 -0.97090976 0.4195 0.06387

164 -0.97151280 0.3577 0.06207

165 -0.97092638 0.4178 0.06040

166 -0.97149664 0.3593 0.05870

167 -0.97094210 0.4162 0.05711

168 -0.97148136 0.3609 0.05551

169 -0.97095697 0.4147 0.05401

170 -0.97146690 0.3624 0.05249

171 -0.97097103 0.4132 0.05107

172 -0.97145324 0.3638 0.04964

173 -0.97098432 0.4119 0.04829

6

174 -0.97144031 0.3651 0.04694

175 -0.97099689 0.4106 0.04567

176 -0.97142809 0.3663 0.04439

177 -0.97100878 0.4094 0.04318

178 -0.97141653 0.3675 0.04198

179 -0.97102002 0.4082 0.04083

180 -0.97140561 0.3687 0.03969

181 -0.97103065 0.4071 0.03861

182 -0.97139527 0.3697 0.03754

183 -0.97104070 0.4061 0.03651

184 -0.97138550 0.3707 0.03550

185 -0.97105021 0.4051 0.03453

186 -0.97137626 0.3717 0.03357

187 -0.97105919 0.4042 0.03265

188 -0.97136752 0.3726 0.03174

189 -0.97106769 0.4033 0.03088

190 -0.97135925 0.3734 0.03002

191 -0.97107573 0.4025 0.02920

192 -0.97135144 0.3742 0.02838

193 -0.97108333 0.4017 0.02761

194 -0.97134405 0.3750 0.02684

195 -0.97109052 0.4010 0.02611

196 -0.97133706 0.3757 0.02538

197 -0.97109731 0.4003 0.02469

198 -0.97133045 0.3764 0.02400

199 -0.97110374 0.3996 0.02335

200 -0.97132420 0.3770 0.02270

201 -0.97110982 0.3990 0.02208

202 -0.97131830 0.3776 0.02146

203 -0.97111557 0.3984 0.02088

204 -0.97131271 0.3782 0.02030

205 -0.97112100 0.3978 0.01974

206 -0.97130742 0.3787 0.01919

207 -0.97112614 0.3973 0.01867

208 -0.97130243 0.3792 0.01815

209 -0.97113100 0.3968 0.01765

210 -0.97129770 0.3797 0.01716

211 -0.97113559 0.3963 0.01669

212 -0.97129323 0.3802 0.01623

213 -0.97113994 0.3959 0.01579

214 -0.97128901 0.3806 0.01535

215 -0.97114405 0.3955 0.01493

216 -0.97128501 0.3810 0.01451

217 -0.97114793 0.3951 0.01412

218 -0.97128123 0.3814 0.01372

219 -0.97115161 0.3947 0.01335

220 -0.97127766 0.3818 0.01298

221 -0.97115508 0.3944 0.01262

222 -0.97127428 0.3821 0.01227

223 -0.97115837 0.3940 0.01194

224 -0.97127109 0.3825 0.01161

225 -0.97116148 0.3937 0.01129

226 -0.97126807 0.3828 0.01097

227 -0.97116441 0.3934 0.01067

228 -0.97126521 0.3831 0.01038

229 -0.97116719 0.3931 0.01009

230 -0.97126251 0.3833 0.00981

7

GRAFICA RAIZ POSITIVA: x=-2:0.001:3; y=-0.9*x.^2+1.7*x+2.5; plot(x,y), grid, title('y=-0.9*x.^2+1.7*x+2.5');

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3-5

-4

-3

-2

-1

0

1

2

3

4

X: 2.862

Y: -0.00654

y=-0.9*x.2+1.7*x+2.5

PUNTO FIJO:

clc; et=0; ea=100; es=0.01; vv=2.862; x=5.0; i=0; disp (' i x et ea') while es < ea, et=abs(((vv-x)/vv)*100); if i~=0; ea=abs((x-xa)/x)*100; end xa=x; fprintf('%2.0f %9.8f %5.4f %4.5f\n' , i,x,et,ea); x=sqrt((1.7*x+2.5)/0.9); i=i+1; end

RESULTADOS: i x et ea 0 5.00000000 74.7030 100.00000 1 3.49602949 22.1534 43.01939 2 3.06290533 7.0198 14.14096 3 2.92630580 2.2469 4.66799 4 2.88188207 0.6947 1.54148 5 2.86728666 0.1847 0.50903 6 2.86247510 0.0166 0.16809 7 2.86088713 0.0389 0.05551

8

8 2.86036286 0.0572 0.01833 9 2.86018975 0.0633 0.00605

METODO NEWTON-RAPHSON RAIZ NEGATIVA: clc; et=0; ea=100; es=0.01; vv=-0.975; x=-1; i=0; disp ('i x et ea') while es < ea, et=((vv-x)/vv)*100; if i~=0; ea=abs((x-xa)/x)*100; end xa=x; fprintf('%2.0f %9.7f %5.4f %5.4f\n' , i,x,et,ea); x=xa-((-0.9*x.^2+1.7*x+2.5)/(-1.8*x+17)); i=i+1; end i x et ea 0 -1.0000000 -2.5641 100.0000 1 -0.9946809 -2.0185 0.5348 2 -0.9903484 -1.5742 0.4375 3 -0.9868184 -1.2121 0.3577 4 -0.9839413 -0.9171 0.2924 5 -0.9815959 -0.6765 0.2389 6 -0.9796834 -0.4804 0.1952 7 -0.9781238 -0.3204 0.1594 8 -0.9768518 -0.1899 0.1302 9 -0.9758142 -0.0835 0.1063 10 -0.9749678 0.0033 0.0868 11 -0.9742772 0.0741 0.0709 12 -0.9737138 0.1319 0.0579 13 -0.9732541 0.1791 0.0472 14 -0.9728791 0.2175 0.0386 15 -0.9725730 0.2489 0.0315 16 -0.9723233 0.2745 0.0257 17 -0.9721195 0.2954 0.0210 18 -0.9719532 0.3125 0.0171 19 -0.9718175 0.3264 0.0140 20 -0.9717068 0.3378 0.0114 21 -0.9716164 0.3470 0.0093

9

METODO NEWTON-RAPHSON RAIZ POSITIVA:

clc; et=0; ea=100; es=0.01; vv=2.862; x=-1; i=0; disp ('i x et ea') while es < ea, et=((vv-x)/vv)*100; if i~=0; ea=abs((x-xa)/x)*100; end xa=x; fprintf('%2.0f %9.7f %5.4f %5.4f\n' , i,x,et,ea); x=xa-((-0.9*x.^2+1.7*x+2.5)/(-1.8*x+17)); i=i+1; end i x et ea 0 -1.0000000 134.9406 100.0000 1 -0.9946809 134.7547 0.5348 2 -0.9903484 134.6034 0.4375 3 -0.9868184 134.4800 0.3577 4 -0.9839413 134.3795 0.2924 5 -0.9815959 134.2975 0.2389 6 -0.9796834 134.2307 0.1952 7 -0.9781238 134.1762 0.1594 8 -0.9768518 134.1318 0.1302 9 -0.9758142 134.0955 0.1063 10 -0.9749678 134.0660 0.0868 11 -0.9742772 134.0418 0.0709 12 -0.9737138 134.0221 0.0579 13 -0.9732541 134.0061 0.0472 14 -0.9728791 133.9930 0.0386 15 -0.9725730 133.9823 0.0315 16 -0.9723233 133.9736 0.0257 17 -0.9721195 133.9664 0.0210 18 -0.9719532 133.9606 0.0171 19 -0.9718175 133.9559 0.0140 20 -0.9717068 133.9520 0.0114 21 -0.9716164 133.9489 0.0093