Métodos númericos

Programa 1

xi=0; xs=14; xr=0;

es=0.1; iter=1; bandera=100;

while bandera>es, xrold=xr;

fxi=(exp(-xi) ;

xr=(xi+xs)/2;

er=abs((xr-xrold)/xr)*(100);

printf('Iteracion = %2.0f     xl= %2.5f     xu= %2.5f     xr= %2.5f     er= %3.5f \n', iter, xi, xs, xr, er);

fxr=(xr)^(10) -1;

test=fxi*fxr; if test < 0 then xs=xr;

elseif test > 0 then xi=xr;

else break; end;

if er < es then bandera=er;

else iter=iter+1;

end;

end

Programa 2 de la regla falsa:

xi=0; xs=1; xr=0;

es=0.01; iter=1; bandera=100;

while bandera>es, xrold=xr;

fxs=(exp(-xs)-xs);

fxi=(exp(-xi)-xi);

xr=((xs*fxi)-(xi*fxs))/(fxi-fxs);

er=abs((xr-xrold)/xr)*(100);

printf('Iteracion = %2.0f     xi= %2.5f     xs= %2.5f     xr= %2.5f     er= %3.5f \n', iter, xi, xs, xr, er);

fxr=(exp(-xr)-xr);

test=fxi*fxr; if test < 0 then xs=xr;

elseif test > 0 then xi=xr;

else break; end;

if er < es then bandera=er;

else iter=iter+1;

end;

end

PROGRAMA 3 DE FALSA POSiCION

xi=0; xs=1.3; xr=0;

es=0.1; iter=1; bandera=100;

while bandera>;es, xrold=xr;

fxs=(xs)^(10) -1;

fxi=(xi)^(10) -1;

xr=(xs*fxi-xi*fxs)/(fxi-fxs);

er=abs((xr-xrold)/xr)*(100);

printf(‘;Iteracion = %2.0f xl= %2.5f xu= %2.5f xr= %2.5f er= %3.5f \n’;, iter, xi, xs, xr, er);

fxr=(xr)^(10) -1;

test=fxi*fxr; if test < 0 then xs=xr;

elseif test > 0 then xi=xr;

else break; end;

if er < es then bandera=er;

else iter=iter+1;

end;

end

PROGRAMA 4 DE FALSA POSICIÓN CON BISECCION

xi=0; xs=1.3; xr=0;

es=0.01; iter=1; bandera=100;

while bandera>es, xrold=xr; xr= ((xi+xs)/2)

er=abs((xr-xrold)/xr)*(100);

printf('Iteracion = %2.0f     xi= %2.5f     xs= %2.5f     xr= %2.5f     er= %3.5f \n', iter, xi, xs, xr, er);

fxr=((xr^(10))-1);

fxi=((xi^(10))-1);

test=fxi*fxr; if test < 0 then xs=xr;

elseif test > 0 then xi=xr;

else break; end;

if er < es then bandera=er;

else iter=iter+1;

end;

end

PROGRAMA 5 FALSA POSICION MODIFICADA

xl=0; xu=1.3; xr=0; fxl=0; fxu=0 ;fxr=0; imax=100; iu=0; il=0;

es=0.01; iter=1; bandera=100;

fxl= ((xl)^10)-1;

fxu= ((xu)^10)-1;

while bandera>es, xrold=xr;

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

fxr= ((xr)^10)-1;

er=abs((xr-xrold)/xr)*(100);

printf('Iteracion =%2.0f xi=%2.5f xs= %2.5f xr= %2.5f er= %3.5f \n', iter, xl, xu, xr, er);

test=fxl*fxr;

if test < 0 then

xu=xr;

fxu= ((xu)^10)-1;

iu=0;

il=il+1;

if il >= 2 then fxl=fxl/2;

end;

elseif test > 0 then

xl=xr;

fxl=((xl)^10)-1;

il=0;

iu=iu+1;

if iu>=2 then fxu= fxu/2;

end;

end;

if er < es then bandera=er;

else iter=iter+1;

end;

if iter >= imax then break;

end;

end

PROGRAMA 6 PUNTO FIJO

xr=0; iter=0; bandera=100; es=0.1;

while bandera>es, xrold=xr;

xr=exp(-xrold);

iter=iter + 1;

ea=abs(((xr-xrold)/xr))*100;

printf('iteracion=%2.0f   xr=%2.5f   xrold=%3.5f   ea=%3.5f\n', iter  , xr  , xrold  , ea);

if ea

end;

end

PROGRAMA 7 DE NEWTON-RAPHSON

xr=0; iter=0; bandera=100; es=0.1;

while bandera>es, xrold=xr;

 xr=xrold -((exp(-xrold)- xrold)) /((-exp(-xrold)-1));

iter=iter + 1;

ea=abs(((xr-xrold)/xr))*100;

printf('iteracion=%2.0f   xr=%2.5f   xrold=%3.5f   ea=%3.5f\n', iter  , xr  , xrold  , ea);

if ea

end;

end

PROGRAMA 8 SECANTE

xr=0; iter=0; bandera=100; es=0.1;

xrold=1;

xr2old=0;

while bandera>es;

fxr2old=((exp(-xr2old))- xr2old);

fxrold=((exp(-xrold))-xrold);

xr=((xrold*fxr2old)-(xr2old*fxrold))/(fxr2old-fxrold);

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