disp ('                This is the code of Muller method.Is written by Ali Ashouri')
disp (' ')
disp (' ')
disp ('    ********Before enter anything read all of introduction that will write. read all of them*******')
disp (' ')
format long
disp ('                 x must be at double class . like: x=-1:0.00001:1')
disp (' ')
disp ('                 function should be start by @(x) like : @(x) sin(x)')
disp (' ')
x=input(' enter your variable for x : ');
f=input('enter your function:  ');
k=input('enter the first number of limit : ');
l=input('enter the final number of limit: ');
d=input('Enter the epsilon or d number :  ');
tic
disp (' ')
disp (' ')
double (x);
n=1;
x2=k;
x1=l;
x0=(x1+x2)./2;
q=(x0-x1)/(x1-x2);
a=q.*f(x0)-q*(1+q)*f(x1)+(q.^2)*(f(x2));
b=(2*q+1)*f(x0)-((1+q).^2)*f(x1)+(q.^2)*f(x2);
c=(1+q)*f(x0);
D=sqrt(b.^2-4*a*c);
if abs(b+D) > abs(b-D),
        E = b+D;
    else
        E = b-D;
end;
xn=x0-(x0-x1)*2*c./(E);
xn=real(xn);
W={'n' ' ' 'min' ' ' 'max' ' ' 'x0' ' ' 'xn'};
B={n ' ' num2str(x2) ' ' num2str(x1) ' ' num2str(x0) ' ' num2str(xn) };
while abs(f(xn))>=d
    n=n+1;
   if xn>x0
       x2=x0;
       x0=xn;
   else
       x1=x0;
       x0=xn;
   end;
   q=(x0-x1)/(x1-x2);
   a=q.*f(x0)-q*(1+q)*f(x1)+(q.^2)*(f(x2));
   b=(2*q+1)*f(x0)-((1+q).^2)*f(x1)+(q.^2)*f(x2);
   c=(1+q)*f(x0);
   D=sqrt(b.^2-4*a*c);
   if abs(b+D) > abs(b-D),
       E = b+D;
   else
       E = b-D;
   end;
   xn=x0-(x0-x1)*2*c./(E);
   xn=real(xn);
   A(n-1,1)={n};
   A(n-1,2)={' '};
   A(n-1,3)={num2str(x2)};
   A(n-1,4)={' '};
   A(n-1,5)={num2str(x1)};
   A(n-1,6)={' '};
   A(n-1,7)={num2str(x0)};
   A(n-1,8)={' '};
   A(n-1,9)={num2str(xn)};
end;
F={'-------'  '--------' '------' '-------' '-------' '--------' '---------' '--------------' '---------------'};
 Q=[W ; F ; B ; A];
 disp(Q)
 disp(' ')
 disp([' The answer is : ',num2str(cell2mat(Q(n+2,9)))])
 disp (['                          n=',num2str(n)])
 disp(' ')
 toc;