Undefined function or variable 'fr' and 'xm'

Hello, I am trying to do this exercise of finding a root by using the bisection method and the false position method. But, when compiling, it keeps saying this error. Can someone help me?

the code:

clear all clc

f =@(x)(1.67*cos(40.0))-(2.5*cos(x))+(1.83-cos((40.0-x)));

a0=input('Entre com a primeira aproximação a0:');

b0=input('Entre com a segunda aproximação b0:');

tol=input('Entre com o valor da tolerancia:');

 while (abs(b0-a0)>tol)
     xm =(a0+b0)/2;
     if((f(a0)*f(xm)<0))
         b0=xm
     else
         a0=xm
     end
 end
fprintf("A Raiz da equação pelo método da bissecção é= %f\n", xm);

 %Regula Falsi
 f1 = f(a0)
 f2= f(b0)

 while (abs(b0-a0)>tol)
     fr = (((a0)*f1)-((b0)*f2))/(f2-f1);
     y=f(fr);
     if((f1*y>0))
         a0=fr;
         f1=y;
     else
         b0=fr;
         f2=y;
     end
  end
 fprintf("%f",fr);

Answer 1

[James Tursa]

Your bisection method changes a0 and b0, which are then fed into your false position method as the starting point. You need to remember the starting point and make sure you feed that same starting point into both methods.

Also, it a0 and b0 are really good guesses and pass the tol test immediately, you never set xm or fr.