close all     % closes all windows opened during the previous runs
clear all     % clears the memory from the results of previous runs
clc           % clears screen
nx=           % THE NUMBER OF POINTS IN X DIRECTION
dx=           % DISCRETISATION STEP
x=            % X-COORDINATES OF GRID POINTS
kap=          % THERMAL DIFFUSIVITY
dt=           % OPTIMAL TIME STEP
t=            % INITIAL TIME
tend=         % FINAL TIME
u0=           % INITIAL CONDITION
u=u0;         % MEMORY ALLOCATION FOR THE SOLUTION AT THE NEXT TIME STEP
alp=0
bet=0
it=0;
plot(x,u,'r')  % plots initial temperature
hold on;       % enables overplotting
nt=50;         % defines the frequency of lines on the plot
while t<tend
   t=t+dt;         % new time
   it=it+1;        % counts time steps 
   u(1)=           % LEFT BC
   for i=2:nx-1
      u(i)=        % SOLVES FOR INTERIOR POINTS
   end
   u(nx)=          % RIGHT BC, 1st ORDER BACKWARD DIFFERENCE
%   u(nx)=         % RIGHT BC, 2d  ORDER BACKWARD DIFFERENCE
%   u(nx)=         % RIGHT BC, FICTITIOUS POINT APPROACH
   if mod(it,nt)==0% plots the solution for t=nt*dt, 2*nt*dt, ...
      plot(x,u)     
   end
   u0=u;           % updating the solution
end
it               % shows the total number of time steps
t                % shows the actual final time
u'               % prints the solution for the actual final time
plot(x,u,'g')    % plots the final solution