Question

Use bisection to solve for the root of:

f(x) = x + ln(x)

It is known that the solution lies between 0.1 and 1.0

Print out your solution at each iteration.

Answer 1

%%equation is x + ln(x)

%%initial guesses
disp('when x range between 0.1 and 1.0 ');
xl = 0.1;
xu= 1.0 ;
fl = xl + log(xl)/log(exp(1));
fu = xu + log(xu)/log(exp(1));

%now check if the sign of fl and fu are same or different
if(fl*fu >0)
error('initial guessus must evaluate function with different sign');

end
%%ITERATION SOLUTION USING BISECTION METHOD
max_iterration = 50;
accepted_tolerance = 1e-5;

for i = 1 :max_iterration
err = abs(xl - xu);
%finding the new co-ordiante
xnew = (xl + xu)/2;

fnew = xnew + log(xnew)/log(exp(1));

if(fl*fnew > 0 )
xl = xnew
fl = fnew;
else
xu = xnew
fu = fnew;
end

if(abs(err) < accepted_tolerance)
break;
end

end