INSTITUTO TECNOLGICO DE MATEHUALA

MTODOS NUMRICOS SCC-1017

Ingeniera civil

SEMESTRE ENERO-JUNIO 2015

Unidad 2. Ejemplo 5.2 y 5.4

Briones Salazar Francisco

5 de Marzo 2015

TECNOLGICO NACIONAL DE MXICO Instituto Tecnolgico de Matehuala

1.- Enunciado del problema.

2.- Solucin grfica.

x=0:0.0001:1; y=(5*x.^3)-(5*x.^2)+(6*x)-(2); plot(x,y), grid,

title(' y=5*x.^3-5*x.^2+6*x.-2');

3.- Programa en cdigo Matlab para solucin del

problema.

% Problema 5.2 b) Encontrar la raz mas pequea

clc;

format short;

vv=0.4181;

es=0.01; ea=100;

i=1;

xl=0;

xu=1;

x=xl;

fxl=5*x.^3-5*x.^2+6*x-2;

x=xu;

fxl=5*x.^3-5*x.^2+6*x-2;

disp (' i xl xu xr ea et fxl fxu fxr

')

while es < ea;

xr=(xl+xu)/2;

et=((vv-xr)/vv)*100;

if i~=1; ea=(abs((xr-xra)/xr)*100); end

x=xl;

fxl=5*x.^3-5*x.^2+6*x-2;

x=xu;

fxu=5*x.^3-5*x.^2+6*x-2;

x=xr;

fxr=5*x.^3-5*x.^2+6*x-2;

fprintf('%2.0f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f %9.4f

%9.4f\n' , i,xl,xu,xr,ea,et,fxl,fxu,fxr);

if fxl*fxr0; xl=xr; end

xra=xr;

i=i+1;

end

4. - Solucin. Resultado de la ejecucin del programa

Matlab.

i xl xu xr ea et fxl fxu fxr 1 0.0000 1.0000 0.5000 100.0000 -19.5886 -2.0000 4.0000 0.3750 2 0.0000 0.5000 0.2500 100.0000 40.2057 -2.0000 0.3750 -0.7344 3 0.2500 0.5000 0.3750 33.3333 10.3085 -0.7344 0.3750 -0.1895 4 0.3750 0.5000 0.4375 14.2857 -4.6400 -0.1895 0.3750 0.0867 5 0.3750 0.4375 0.4063 7.6923 2.8343 -0.1895 0.0867 -0.0525 6 0.4063 0.4375 0.4219 3.7037 -0.9029 -0.0525 0.0867 0.0168 7 0.4063 0.4219 0.4141 1.8868 0.9657 -0.0525 0.0168 -0.0179 8 0.4141 0.4219 0.4180 0.9346 0.0314 -0.0179 0.0168 -0.0006 9 0.4180 0.4219 0.4199 0.4651 -0.4358 -0.0006 0.0168 0.0081

10 0.4180 0.4199 0.4189 0.2331 -0.2022 -0.0006 0.0081 0.0038 11 0.4180 0.4189 0.4185 0.1167 -0.0854 -0.0006 0.0038 0.0016 12 0.4180 0.4185 0.4182 0.0584 -0.0270 -0.0006 0.0016 0.0005 13 0.4180 0.4182 0.4181 0.0292 0.0022 -0.0006 0.0005 -0.0000 14 0.4181 0.4182 0.4182 0.0146 -0.0124 -0.0000 0.0005 0.0002 15 0.4181 0.4182 0.4181 0.0073 -0.0051 -0.0000 0.0002 0.0001

1.- Enunciado del problema.

2.- Solucin grfica.

x=-2:0.00001:6; y=((-12)-(21*x)+(18*x.^2)-(2.75*x.^3));

plot(x,y), grid, title(' y=-12-21*x+18*x.^2-2.75*x.^3');

3.- Programa en cdigo Matlab para solucin del

problema.

% Problema 5.4 b) Encontrar la raz mas pequea

clc;

format short;

vv=-0.4147;

i=1;

es=0.01;ea=100;

xl=-1; xu=0;

x=xl;

fxl=-12-21*x+18*x.^2-2.75*x.^3;

x=xu;

fxu=-12-21*x+18*x.^2-2.75*x.^3;

disp (' i xl xu xr ea et fxl fxu fxr')

while es < ea,

xr= xu-((fxu*(xl-xu))/(fxl-fxu));

x=xr;

fxr=-12-21*x+18*x.^2-2.75*x.^3;

et=((vv-xr)/vv)*100;

if i~=1; ea=abs(((xr-xra)/xr)*100); end

fprintf('%2.0f %6.3f %6.3f %9.4f %9.3f %9.3f %9.2f %9.2f

%9.2f\n' , i,xl,xu,xr,ea,et,fxl,fxu,fxr);

if fxl*fxr0; xl=xr; fxl=fxr; end

xra=xr;

i=i+1;

end

4. - Solucin. Resultado de la ejecucin del programa

Matlab.

i xl xu xr ea et fxl fxu fxr 1 -1.000 0.000 -0.2874 100.000 30.691 29.75 -12.00 -4.41 2 -1.000 -0.287 -0.3794 24.252 8.500 29.75 -4.41 -1.29 3 -1.000 -0.379 -0.4052 6.363 2.283 29.75 -1.29 -0.35 4 -1.000 -0.405 -0.4122 1.684 0.609 29.75 -0.35 -0.09 5 -1.000 -0.412 -0.4140 0.446 0.164 29.75 -0.09 -0.02 6 -1.000 -0.414 -0.4145 0.118 0.045 29.75 -0.02 -0.01 7 -1.000 -0.415 -0.4146 0.031 0.014 29.75 -0.01 -0.00 8 -1.000 -0.415 -0.4147 0.008 0.006 29.75 -0.00 -0.00