can anyone help me to fixed this error in my code?

Index exceeds matrix dimensions.

Error in fun (line 33)
    f(1) = C_avg(i) - Cin(i) + (2 * J(i) /R * dtau);

Error in fsolve (line 230)
            fuser = feval(funfcn{3},x,varargin{:});

Error in main (line 21)
answ = fsolve(@fun,x0,options);

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.
 
>> 




function f = fun(x0)


global tau_max N_tau x_max R N_x dx K1 K2


%initial guess


C_avg =x0(1);
J =x0(2);


C_avg = zeros(N_tau,1);                 %prolocating raw vector
C = zeros(1,N_x);                       %prolocating colum vector

% C_avg is average value of colum vector which is given by equation f(2)
%C is the coulmn vector values

for i = 2:N_tau
    
    
    for k =1:N_x
        if i ==2
        Cin(i) =208;
    
        else
        Cin(i) = C_avg(i-1);
        end
        
    dtau = tau_max/ (N_tau -1);
    f(1) = C_avg(i) - Cin(i) + (2 * J(i) /R * dtau);
    f(2) = C_avg(i) - 2 * (sum ( C(i,k)) - C(1,1) - C(1,N_x));    %where C(i,k) is a column vector [N_tau,N_x] and k is 1 to N_x
    f(3) = J(i) + K1 * (C(i,N_x) - C(i,1));                     % difference between first value of colum vector  and last value colum vector.
    f(4) = J(i) - K2*C(i,N_x);
    
    end




end
end


%%script
clc;
global tau_max N_tau x_max R N_x dx K1 K2
options=optimset('Display','off'); 
tau_max =25;
N_tau = 26;
x_max = 0.003;
R = x_max;
N_x = 5;
dx = x_max/(N_x-1);
K1 =  4.42e-6;
K2 =  4.87e-5;
tau =linspace(0,tau_max,N_tau);
x =linspace(0,R,N_x);


x0 = [193.44,0.007];




answ = fsolve(@fun,x0,options);

figure(1)
plot (C_avg,tau)
xlabel('C_avg')
ylabel('tau')

figure(2)
plot(J,tau)
xlabel('J')
ylabel('tau')