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4C

METODO SECANTE

x0 x1 f(x0) f(x1) x2 f(x2)

1 0 0.5 1

-

0.21328

822

0.41210

324

0.14318

201

2 0.5

0.41210

324

-

0.21328

822

0.14318

201

0.44740

839

0.00497

046

f x( ) cos 3x( ) 1+ ex2

−:=

1− 0.5− 0 0.5 1

3−

2−

1−

1

f x( )

x

g x( )x

f x( )d

d:=

g x( ) 3 sin 3 x⋅( )⋅− 2 x⋅ ex2

⋅−→


2/8

3

0.44740

839

0.41210

324

0.00497

046

0.14318

201

0.44867

806

-

0.00013

177

4

0.44867

806

0.41210

324

-

0.00013

177

0.14318

201

0.44864

443

3.4824E-

06

5

0.44864

443

0.41210

324

3.4824E-

06

0.14318

201

0.44864

531

-9.2035E-

08

6

0.44864

531

0.41210

324

-

9.2035E-

08

0.14318

201

0.44864

529

2.4324E-

09

7

0.44864

529

0.41210

324

2.4324E-

09

0.14318

201

0.44864

529

-

6.4284E-

11

8

0.44864

529

0.41210

324

-

6.4284E-

11

0.14318

201

0.44864

529

1.6986E-

12

9

0.44864

529

0.41210

324

1.6986E-

12

0.14318

201

0.44864

529

-4.4631E-

14

10

0.44864

529

0.41210

324

-

4.4631E-

14

0.14318

201

0.44864

529 0

METODO FALSA POSICION

X0 X1 F(X0) F(X1) x2 f(x2)

f(x0)f(x

2)

0 0.5 1

-0.21328

822

0.41210

324

0.24399

941

0.24399

941

0.41210

324 0.5

0.14318

201

-

0.21328

822

0.44740

839

0.34434

745

0.04930

436

0.44740

839 0.5

0.00497

046

-

0.21328

822

0.44860

607

0.34771

849

0.00172

832

0.44860

607 0.5

0.00015

774

-

0.21328

822

0.44864

405

0.34782

536

5.4866E-

05

0.44864

405 0.5

4.9911E-

06

-0.21328

822

0.44864

525

0.34782

874

1.736E-

06

0.44864

525 0.5

1.5791E-

07

-

0.21328

822

0.44864

529

0.34782

885

5.4925E-

08

0.44864

529 0.5

4.9959E-

09

-

0.21328

822

0.44864

529

0.34782

885

1.7377E-

09


3/8

0.44864

529 0.5

1.5806E-

10

-

0.21328

822

0.44864

529

0.34782

885

5.4978E-

11

0.44864

529 0.5

5.0009E-

12

-

0.21328

822

0.44864

529

0.34782

885

1.7395E-

12

0.44864

529 0.5

1.581E-

13

-0.21328

822

0.44864

529

0.34782

885

5.499E-

14

0.44864

529 0.5

5.107E-

15

-

0.21328

822

0.44864

529

0.34782

885

1.7764E-

15

0.44864

529 0.5 0

-

0.21328

822

0.44864

529

0.34782

885 0

Ejercicio

Use el método de Muller para resolver las ecuación:f(x)=ex-3x2

pli!ue cinco iteraciones " determine cómo estan relacionados los errores sucesivos# Utilicevalores iniciales !ue difieran entre s$ por %#2& ra$' cerca de 3#

*+U,./

f x( ) ex

3x2

−:=

0 1 2 3 4

10−

5−

5

10

f x( )

x


4/8

0a iteración

x2 x% x0 f2 f% f0

3#1 3#( 3# -3#34145%4 -%#2214 3#((24400

Ecuación de la par67ola !ue pasa por los puntos (x%&f%)& (x0&f0) " (x2&f2):

" = ax2 8 7x 8 c

M

3.52

3.72

3.92

3.5

3.7

3.9

1

1

1

:= v

3.63454804−

0.62269564−

3.77244911

:=

β lsolve M v,( )

17.29115

109.43705−

167.57848

=:=

9ora& 9allemos las ra$ces de la par67ola

" = 0#2001x2 - 0%#43%1x 8 0#1545

w

β2

β1

β0

167.578

109.437−

17.291

=:=

polyroots w( )2.5964440812

3.7326330369

= xr 3.7326330369:=


5/8

M

3.72

xr 2

3.92

3.7

xr

3.9

1

1

1

:=v

0.62269564−

0.00865277−

3.77244911

:=

2a iteración

x2 x% x0 f2 f% f0

3.7 3.73263304 3.9 -0.62269564 -0.00865277 3.77244911

Ecuación de la par67ola !ue pasa por los puntos (x%&f%)& (x0&f0) " (x2&f2):

" = ax2 8 7x 8 c

β lsolve M v,( )

18.87542

121.47747−

190.43943

=:=


" = 05#5142x2 - 020#44x 8 0%#4343

w

β2

β1

β0

190.439

121.477−

18.875

=:=

polyroo ts w( )2.7026710161

3.7330781161

= v

0.00865277−

0.000017711−

3.77244911

:=


6/8

polyroo ts w( )2.7175973938

3.7330790286

=xr2 3.7330790286:=

β lsolve M v,( )

19.1138

123.29696−

193.90964

=:=


" = 0#0035x2 - 023#2x 8 03#%4

w

β2

β1

β0

193.91

123.297−19.114

=:=


7/8

4ta iteración

x2 x% x0 f2 f% f0

3.73307812 3.73307903 3.9 -1.7711E-05 -6.3689E-10 3.77244911

Ecuación de la par67ola !ue pasa por los puntos (x%&f%)& (x0&f0) " (x2&f2):" = ax2 8 7x 8 c

M

xr12

xr22

3.92

xr1

xr2

3.9

1

1

1

:= v

0.0000177114831600989−

6.36894981198566!10−

3.77244910553017

:=

β lsolve M v,( )

19.11711

123.3222−

193.95779

=:=


" = 0#0000x2 - 023#3222x 8 03#1

w

β2

β1

β0

193.958

123.322−

19.117

=:=

polyroots w( )2.7178019149

3.7330790286

= xr3 3.7330790286:=


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