Ricardo Adolfo GrandasCódigo: 2305014

Ejercicios en Scilab

1) Método 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.\t\t Xa\t\t Xb\t\t Xr\t\t 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);

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; endelse printf('No existe una raíz en ese intervalo');endendfunction

2) Método Newton-Raphson

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;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;endprintf(' 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));endendfunction

3) Iteración Punto Fijofunction 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;endprintf(' i \t X(i) Error aprox (i) \n');for j=1:i; printf('%2d \t %11.7f \t %7.3f \n',j-1,x(j),ea(j));endendfunction

4) a- Newtonfunction 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;endprintf(' 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));endendfunction

b- Secantefunction 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; endprintf(' i \t\t x(i) \t Error aprox (i) \n');printf('%2d \t %11.7f \t \n',0,x(1));for k=2:j; printf('%2d \t %11.7f \t %7.3f \n',k-1,x(k),ea(k-1));endendfunction

5)a- 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 \t\t x(i) \t Error aprox (i) \n');printf('%2d \t %11.7f \t \n',0,x(1));

for k=2:j; printf('%2d \t %11.7f \t %7.3f \n',k-1,x(k),ea(k-1));end

endfunction

b- Falsa Posición

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 %11.7f\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(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 %11.7f\t %7.3f \n', i+1,xa(i+1),xb(i+1),xr(i+1),f(xr(i+1)),ea(i+1)); i=i+1; endelse printf('No existe una raíz en ese intervalo');endendfunction