Taller numero 4 (metodos numericos) desarrollado en scilab. Codigo de los programas

1. ANDRES FELIPE RENTERIA MARTINEZ 2303517
CODIGO DEL PROGRAMA SCILAB
1.) Punto de biseccion
function y=f(x)
y=-12.4+10*(0.5*%pi-asin(x/1)-x*(1-x**2)**0.5);
endfunction
function xr=biseccion(xai,xbi,tol)
i=1;
ea(1)=100;
if f(xai)*f(xbi) < 0
xa(1)=xai;
xb(1)=xbi;
xr(1)=(xa(1)+xb(1))/2;
printf('It.tt Xatt Xbtt Xrtt f(Xr)t Error n');
printf('%2d t %11.7f t %11.7f t %11.7f t %11.7f n',i,xa(i),xb(i),xr(i),f(xr(i)));
while abs(ea(i)) >= tol
if f(xa(i))*f(xr(i))< 0
xa(i+1)=xa(i);
xb(i+1)=xr(i);
end
if f(xa(i))*f(xr(i))> 0
xa(i+1)=xr(i);
xb(i+1)=xb(i);

2. end
xr(i+1)=(xa(i+1)+xb(i+1))/2;
ea(i+1)=abs((xr(i+1)-xr(i))/(xr(i+1)));
printf('%2d t %11.7f t %11.7f t %11.7f t %11.7f t %7.6f
n',i+1,xa(i+1),xb(i+1),xr(i+1),f(xr(i+1)),ea(i+1));
i=i+1;
end
else
printf('No existe una raíz en ese intervalo');
end
endfunction
2.)punto de Newton-Rapson
function y=f(x)
y=2*x**3+x-1;
endfunction
function y=df(x)
y=6*x**2+1;
endfunction
function x=newtonraphson(x0,tol);
i=1;
ea(1)=100;
x(1)=x0;

3. while abs(ea(i))>=tol;
x(i+1)=x(i)-f(x(i))/df(x(i));
ea(i+1)=abs((x(i+1)-x(i))/x(i+1));
i=i+1;
end
printf(' i t X(i) Error aprox (i) n');
for j=1:i;
printf('%2d t %11.7f t %7.6f n',j-1,x(j),ea(j));
end
endfunction
3.) Punto de Interacion del punto fijo
function y=g(x)
y=300-80.425*x+201.0625*(1-exp(-(0.1)*x/0.25));
endfunction
function x=puntofijo(x0,tol)
i=1;
ea(1)=100;
x(1)=x0;
while abs(ea(i))>=tol,
x(i+1) = g(x(i));
ea(i+1) = abs((x(i+1)-x(i))/x(i+1));
i=i+1;
end
printf(' i t X(i) Error aprox (i) n');

4. for j=1:i;
printf('%2d t %11.7f t %7.3f n',j-1,x(j),ea(j));
end
endfunction
4.)
A)Newton
function y=f(x)
y=4*cos(x)-exp(x);
endfunction
function y=df(x)
y=-4*sin(x)-exp(x);
endfunction
function x=newtonraphson(x0,tol);
i=1;
ea(1)=100;
x(1)=x0;
while abs(ea(i))>=tol;
x(i+1)=x(i)-f(x(i))/df(x(i));
ea(i+1)=abs((x(i+1)-x(i))/x(i+1));
i=i+1;
end
printf(' i t X(i) Error aprox (i) n');
for j=1:i;

5. printf('%2d t %11.7f t %7.6f n',j-1,x(j),ea(j));
end
endfunction
B) Metodo de la Secante
function y=f(x)
y=4*cos(x)-exp(x);
endfunction
function x = secante(x0,x1,tol)
j=2;
i=1;
x(1)=x0;
x(2)=x1;
ea(i)=100;
while abs(ea(i))>=tol
x(j+1)=(x(j-1)*f(x(j))-x(j)*f(x(j-1)))/(f(x(j))-f(x(j-1)));
ea(i+1)=abs((x(j+1)-x(j))/x(j+1));
j=j+1;
i=i+1;
end
printf(' i tt x(i) t Error aprox (i) n');
printf('%2d t %11.7f t n',0,x(1));
for k=2:j;

6. printf('%2d t %11.7f t %7.3f n',k-1,x(k),ea(k-1));
end
endfunction
5.)
A) Metodo de la secante
function y=f(x)
y=x**2-6;
endfunction
function x = secante(x0,x1,tol)
j=2;
i=1;
x(1)=x0;
x(2)=x1;
ea(i)=100;
while abs(ea(i))>=tol
x(j+1)=(x(j-1)*f(x(j))-x(j)*f(x(j-1)))/(f(x(j))-f(x(j-1)));
ea(i+1)=abs((x(j+1)-x(j))/x(j+1));
j=j+1;
i=i+1;
end
printf(' i tt x(i) t Error aprox (i) n');
printf('%2d t %11.7f t n',0,x(1));

7. for k=2:j;
printf('%2d t %11.7f t %7.3f n',k-1,x(k),ea(k-1));
end
endfunction
5.)
B)Falsa Posicion
function y=f(x)
y=x**2-6;
endfunction
function xr=reglafalsa(xai,xbi,tol)
i=1;
ea(1)=100;
if f(xai)*f(xbi) < 0
xa(1)=xai;
xb(1)=xbi;
xr(1)=xa(1)-f(xa(1))*(xb(1)-xa(1))/(f(xb(1))-f(xa(1)));
printf('It. Xa Xb Xr f(Xr) Error aprox %n');
printf('%2d t %11.7f t %11.7f t %11.7ft %11.7f n',i,xa(i),xb(i),xr(i),f(xr(i)));
while abs(ea(i))>=tol,
if f(xa(i))*f(xr(i))< 0
xa(i+1)=xa(i);

8. xb(i+1)=xr(i);
end
if f(xa(i))*f(xr(i))> 0
xa(1)=xr(i);
xb(1)=xb(i);
end
xr(i+1)=xa(i+1)-f(xa(i+1))*(xb(i+1)-xa(i+1))/(f(xb(i+1))-f(xa(i+1)));
ea(i+1)=abs((xr(i+1)-xr(i))/(xr(i+1)));
printf('%2d t %11.7f t %11.7f t %11.7f t %11.7ft %7.3f n',
i+1,xa(i+1),xb(i+1),xr(i+1),f(xr(i+1)),ea(i+1));
i=i+1;
end
else
printf('No existe una raíz en ese intervalo');
end
endfunction