i have problem in heat equation 1D

%%  PROJECT 1
%
%Applications problem in chapter 3  problem 3.1 page 96 
%
% $$ Tixt book $$: COMPUTATIONAL FLUID DANAMICS VI 
%
% $$ BY $$ K. A. HAFFMANN
%
%  $$ Cource \# $$ 804416 & 804441
%
%  NAME :ALI MUSTAFA SADEQ ALAIDAROS
%  ID #   435025962
clc
clear all
close all
%% Problem definition 
%A wall 1 ft. thick and infinite in other directions has 
%an initial uniform temperature (??) of 100.0°?. The surface temperature(??) 
%at the two sides are suddenly increased and maintained at 300.0°?
%with a diffusivity of ?=0.1 ??2/?? the unsteady
%one-space dimensional heat conduction time intervals from 0.0 to 0.5 hr.
%% Equation:
% The Equation for this problem may be expressed as:
%
% $$\left( {\partial T \over \partial t} = \alpha {\partial^{2} T \over \partial x^{2} } \right) $$   

%% Boundary Codition
% $$u(0,t) = 300 F $$
%
% $$u(L,t) = 300 F $$
%% Initial condition
% $$  u(x,0) = 100.0 F $$            for      $$0 < x \ L $$
%
% $$u(x,0) = 300 F $$            for     $$x = 0$$  
% $$u(x,0) = 300 F $$            for     $$x = L$$
%% Solution Method: the DuFort-Frankel Explicit Method 
%  U(n+1,i) = ((1-B).*U(n-1,i) + B .* ( U(n,i+1) + U(n,i-1))./(1+B)

%% Constants declaration 
 TMAX    = 0.5 ;                    % Maximum time in hour 
 DT      = [0.01 0.005 0.0001] ;                  % time step
 %NM      = [((TMAX/DT(1)) + 1)  ((TMAX/DT(2)) + 1)];           % # of step in time
 alpha      = 0.1;                % diffusivity constant
 L = 1;                  % the wall lenght
 DX     = 0.05;                    % step in x
 IM      = L/DX + 1;          % # of step in x-direction
 
% B       = [(2.*alpha.*DT(1) / (DX.^2))  (2.*alpha.*DT(2) / (DX.^2))];       % The stability requirement
 xx = 0:DX:L;
u      = zeros(IM) ;
tp = 0:0.1:0.5
 %tp =[0.1 0.2 0.3 0.4 0.5]
%% Solution  

     

     % Numerical solution
     % ------------------------
   
             
        T(1)=300;            %boundry condition
        T(IM)=300;           %boundry condition
        TO(1)=300;
        TO(IM)=300;
        T((2:IM-1))=100;      %initial conditional
        TO((2:IM-1))=100;
    

%%%%%%%%%%%%%                                            

% Solution using DuFort-Forankel Method

for dt=1:2
    
  NM(dt)      = ((TMAX/DT(dt)) + 1);
  B(dt)       = (2.*alpha.*DT(dt) / (DX.^2));
for  K=1:NM(dt)
for I=1:IM
TOO(I) = TO(I);
TO(I) = T(I);
TP(I,K) = T(I);
end
for I=2:(IM-1)  
T(I)= ( (1 - B(dt))*TOO(I) + B(dt)*( TO(I+1) + TO(I-1) ) ) / ( 1 + B(dt) );
end % myFct: function of the method Dufort-Frankel

end
 

%% Printing data to file
fprintf('%5s %5s %5s  %5s  %5s %5s  \n',...
    'xx','T(I,0.1)','T(I,0.2)',' TP(I,0.3)',' TP(I,0.4)',' TP(I,0.5)'); 
fprintf('=======================================================================================================\n');

for I=1:IM

  
  TT(I,1) = TP(I,dt*1);
  TT(I,2) = TP(I,dt*10);
  TT(I,3) = TP(I,dt*20);
  TT(I,4) = TP(I,dt*30);
  TT(I,5) = TP(I,dt*40);
  TT(I,6) = TP(I,dt*50);

  fprintf('%6.4f %7.3f %7.3f %7.3f %12.8f %12.8f %12.8f  \n',...
      xx(I), TT(I,1), TT(I,2), TT(I,3), TT(I,4), TT(I,5), TT(I,6)) 

end
hold on
for i=1:6
 subplot(1,2,dt)

    plot(xx,TT(:,i))
    
    xlabel('the wall thickness in foot') 
     ylabel('T (Fahrenheit)' )
 title('TEMPERTURE,DX=0.05,DT=0.01.')
 legend('t = 0.0 hour','t = 0.1 hour','t = 0.2 hour','t = 0.3 hour','t = 0.4 hour','t = 0.5 hour')
title('TEMPERTURE,DX=0.05,DT=0.005.')
 
 
 
hold off
 hold all
end 
end

[Geoff Hayes]

Ali's tags moved here

i solve it by dufort franklen method explicit i took two step in time and i try to put it in one loop but i struggle to put it in two plot because in publish i get error in legand and

y label

i used subplot to make to loop the plot

hope to help me as fast you can

thanks

[Geoff Hayes]

Ali - please use comments to add notes to your question (rather than using the tags).

[Ali Alaidaros]

when i run i got two drawing in one plot how to name the x and y axix for each one in same plot

Answer 1

[Geoff Hayes]

Ali - in the future, please include the error message (if any) that you are observings and be as descriptive as possible...because it is unclear what I get error in legend and y label actually means.

When I run your code, i observe the following warnings

Warning: Ignoring extra legend entries. 
> In legend at 290
  In *** at 106 
Warning: Ignoring extra legend entries. 
> In legend at 290
  In *** at 106 
Warning: Ignoring extra legend entries. 
> In legend at 290
  In *** at 106 
Warning: Ignoring extra legend entries. 
> In legend at 290
  In *** at 106 
Warning: Ignoring extra legend entries. 
> In legend at 290
  In *** at 106

This is because you are calling legend with all the diffferent labels before you have added all the curves to the subplot. Updating the title, legend, axes labels should occur after you have drawn your curves so that you don't repeat the set of code six times (and avoid the warnings like above). Try simplifying the code to just

    subplot(1,2,dt)
    plot(xx, TT);
    xlabel('the wall thickness in foot') 
    ylabel('T (Fahrenheit)' )
    title('TEMPERTURE,DX=0.05,DT=0.01.')
    legend('t = 0.0 hour','t = 0.1 hour','t = 0.2 hour','t = 0.3 hour','t = 0.4 hour','t = 0.5 hour')
    title('TEMPERTURE,DX=0.05,DT=0.005.')

Note how there is no loop (which isn't really necessary) and that no warnings appear in the console.

[Ali Alaidaros]

thanks i simplify it ,it's work ,no warrning