How can I turn this Explicit method code to Implicit method code ?

I want to turn my matlab code for 1D heat equation by explicit method to implicit method. How can I do this easily?

% A program to plot the temperature distribution in a insulated rod using the explicit Finite Central Difference Method and 1D Heat equation. 
The rod is heated on one end at 400K and exposed to ambient temperature on the right end at 300K. I am using a time of 10s, 20 grid points 
and a .2s time step. 

 L=1;          %   Length of modeled domain [m]
 t=10;         %   time   [s]
 k=.001;       
 n=20;         %   Number of gridpoints
 nt=500;
 dx=L/n;       %   Spacing of grid
 dt=.2;        %   Timestep [s]
 alpha=k*dt/dx^2;
 T0=400*ones(1,n);
 T1=300*ones(1,n);
 T0(1) = 300;
 T0(end) = 300;

 for j=1:nt
    for i=2:n-1
        T1(i)=T0(i)+(alpha*(T0(i+1)-2*T0(i)+T0(i-1)));
    end
    T0=T1;
 end

 dlmwrite('Trial_1.csv',T1,'Delimiter','\n')  % Saves data into a csv file

Please help.

Answer 1

[Torsten]

    L = 1;          %   Length of modeled domain [m]
    nx = 200;         %   Number of gridpoints
    t = 500;         %   time   [s]
    nt = 15;
    k = .001;       
    dx = L/(nx-1);       %   Spacing of grid
    dt = t/nt;        %   Timestep [s]
    alpha = k*dt/dx^2;
    T0 = 400*ones(nx,1);
    T1 = 300*ones(nx,1);
    T0(1)= 300;
    T0(end) = 300;
    A = full(gallery('tridiag',nx-2,-alpha,1+2*alpha,-alpha));
    for j = 1:nt
      b = [T0(2)+alpha*T0(1);T0(3:nx-2);T0(end-1)+alpha*T0(end)];
      T1(2:end-1) = A\b;
      T0 = T1;
    end

[Md Badrul Hasan]

 A = full(gallery('tridiag',nx-2,-alpha,1+2*alpha,-alpha));
    for j = 1:nt
      b = [T0(2)+alpha*T0(1);T0(3:nx-2);T0(end-1)+alpha*T0(end)];
      T1(2:end-1) = A\b;

I could not understand the operation here. Can you please elaborate ? Thanks for your reply.

[Torsten]

Read and learn:

https://en.wikipedia.org/wiki/Finite_difference_method#Implicit_method

Best wishes

Torsten.