How can you do an inner and outer loop with different convergence criteria ?

I have attempted to solve a non linear PDE using the attached algorithm from the pic. I am struggling to implement in particular step 4 and 5 to do the outer loop. Please could you help me to solve that particular problem?? Thanks in advance.

clear;

clc

% initialise number of nodes
L=10,

M=21; % number of x  nodes 
dx=L/(M-1); 

x=linspace(0,L,M) % discreet x values 

T_alpha=200;

h_p=0.05;

Alpha_p=2.7*10^-9;

% initialise Guess 

u=linspace(0,400,M);

% initialise Boundary conditions

u(1)=300;% right boundary 

u(M)=400; % top boundary 

% calculate temperature distribution 
% 
% for i=2:M-1
% 
% end
 err=1

for k=1:100

      flag=1;
  while flag==1      
         flag=0;
         uold = u

         % step 3
      for i=2:M-1

          f(i)=uold(i-1)-((2+dx^2*h_p)*uold(i))-(dx^2*Alpha_p*uold(i)^4+uold(i+1)+(dx^2*(h_p*T_alpha+Alpha_p*T_alpha^4)))
          u(i)=(f(i)+uold(i-1)+uold(i+1))/(2+dx^2*h_p)+(4*dx^2*Alpha_p*(uold(i))^3);
              error=abs(u(i)-uold(i))/uold(i);                     
              if error > 10^-2
                  flag=1
              end  

      end
  end
  end

plot(x,u,'rp--')