How to write proper convergence criteria?

I am writing a code to simulate the similarity solution for flow over a flat plate. I input some guess value for df2deta2 and want the code to run until it satisfies the boundary condition dfdeta=1 and eta_max. Even when the criteria is not met inside the while loop, it will still output a graph. This is my code so far:

clear all;

eta_max=10;
N=101;
Delta_eta=eta_max/(N-1);

for i=1:N
    eta(i)=(i-1)*Delta_eta;
end

f=zeros(1,N);
dfdeta=zeros(1,N);
df2deta2g=zeros(1,N);

for i=1:N
    df2deta2g(i)=0.2;
end

tol=0.01;
err=2*tol;

while (err>tol)

          f(1)=-0.2;
          dfdeta(1)=0;
          df2deta2g(1)=0.3;            %guess value for df2deta2

      for i=1:(N-1)

          f(i+1)=f(i)+(dfdeta(i)+dfdeta(i+1))*Delta_eta/2;
          dfdeta(i+1)=dfdeta(i)+(df2deta2g(i)+df2deta2g(i+1))*Delta_eta/2;
          df2deta2g(i+1)=df2deta2g(i)-(2*f(i)*df2deta2g(i)+2*f(i+1)*df2deta2g(i+1))*Delta_eta/2;   

      end

      dfdeta(N)=1;

      dfdeta=dfdeta+(df2deta2g+df2deta2g)*Delta_eta/2;

      err=(1-max(dfdeta));

      df2deta2=df2deta2g;

end