Undefined function or variable 'p'. Error in test1 (line 32) px(j)=p(21,j);

n=41;     h=1/(n-1);    nt=360;           tau=0.001;
for i=1:n 
    x(i)=(i-1)*h;
    y(i)=(i-1)*h;  
end  
for j=1:n
    for i=1:n 
        p0(i,j)=1;    
    end   
end
tic
for jt=1:nt 
    t(jt)=jt*tau; 
    for j=1:n   % Anlitik yechimni hisoblash
        for i=1:n 
            pt(i,j)=exp(-2*x(i)*y(j)*t(jt));
        end      
    end 
end

for jt=1:nt/2    % Vaqt bo`yicha tsikl}          
    
    fxy(n,tau,h,p0,x,y,t,jt);
    fyx(n,tau,h,p0,x,y,t,jt);
end % jt
toc

Elapsed time is 0.458155 seconds.

for j=1:n
    px(j)=p(21,j); 
    pxt(j)=pt(21,j);
end                 

Unrecognized function or variable 'p'.

x=0:h:1;
y=0:h:1;
figure ('Position',[600 160 700 600]); %Natijalarni figuraga chiqarish oynasi: 750-eni, 650-boyi, 700-chapdan masofa, 75-yuqoridan masofa  
subplot(3,2,1);

meshc(x,y,pt) %Uch o'lchovli 3D grafika
title('АНИК ЕЧИМ 3D ГРАФИГИ')

subplot(3,2,2);
meshc(x,y,p) %Uch o'lchovli 3D grafika
title('CОНЛИ ЕЧИМ 3D ГРАФИГИ')

subplot(3,2,3);
contour(x,y,pt,'ShowText','on','LineWidth',2); %kontur chizish 
title('АНИК ЕЧИМ КОНТУР ГРАФИГИ')

subplot(3,2,4);
contour(x,y,p,'ShowText','on','LineWidth',2); %kontur chizish 
title('CОНЛИ ЕЧИМ КОНТУР ГРАФИГИ')

subplot(3,2,5);
plot(x,px,x,pxt); %Ikki o'lchovli grafika 
title('КЕСИМДА АНИК ВА CОНЛИ ЕЧИМ ЎЗГАРИШИ X БЎЙИЧА')

function [p0,p] = fxy(n,tau,h,p0,x,y,t,jt)

% k+0.5 vaqt qatlamida hisoblash
for j=2:n-1     % Tenglamalar koeffitsientini hisoblash 
    for i=2:n-1  
        %chekli ayirma tenglama koeffitsentlarini hisoblash  
        a(i)=1;
        c(i)=1;
        b(i)=2+2*h*h/tau;
        ff=h*h*(-2*(2*t(jt)*t(jt)*(x(i)*x(i)+y(j)*y(j))+x(i)*y(j))*exp(-2*x(i)*y(j)*t(jt)));   
        d(i)=2*h*h/tau*p0(i,j)+(p0(i,j-1)-2*p0(i,j)+p0(i,j+1))+ff;  
    end
    %Pragonka koeffitsentlarini hisoblash 
    aa1(1)=0; bb1(1)=1;    
    for i=2:n-1
        aa1(i)=c(i)/(b(i)-aa1(i-1)*a(i));
        bb1(i)=(d(i)+bb1(i-1)*a(i))/(b(i)-aa1(i-1)*a(i));
    end
    % bosim funktsiyasini hisoblash   
    p(n,j)=exp(-2*y(j)*t(jt));  
    for i=n-1:-1:1 
        p(i,j)=aa1(i)*p(i+1,j)+bb1(i);
    end                   
end %j    

for i=1:n % Chegaraviy qiymatlarni hisoblash 
    p(i,n)=(4.0*p(i,n-1)-p(i,n-2))/3;
    p(i,1)=(4.0*p(i,2)-p(i,3))/3;
end      

for j=1:n  % k+1 qatlam uchun boshlangich qiymatni hisoblash  
    for i=1:n      
        p0(i,j)=p(i,j);  
    end  
end         

% k+1 vaqt qatlamida hisoblash
for i=2:n-1    % Tenglamalar koeffitsientini hisoblash 
    for j=2:n-1  
        %chekli ayirma tenglama koeffitsentlarini hisoblash       
        a(j)=1;
        c(j)=1;
        b(j)=2+2*h*h/tau;
        ff=h*h*(-2*(2*t(jt)*t(jt)*(x(i)*x(i)+y(j)*y(j))+x(i)*y(j))*exp(-2*x(i)*y(j)*t(jt)));   
        d(j)=2*h*h/tau*p0(i,j)+(p0(i-1,j)-2*p0(i,j)+p0(i+1,j))+ff; 
    end
    %Pragonka koeffitsentlarini hisoblash 
    aa1(1)=0; bb1(1)=1;  
    for j=2:n-1 
        aa1(j)=c(j)/(b(j)-aa1(j-1)*a(j));
        bb1(j)=(d(j)+bb1(j-1)*a(j))/(b(j)-aa1(j-1)*a(j));
    end
    % bosim funktsiyasini hisoblash   
    p(i,n)=exp(-2*x(i)*t(jt));  
    for j=n-1:-1:1 
        p(i,j)=aa1(j)*p(i,j+1)+bb1(j);
    end    
end  %i             

for j=1:n  % Chegaraviy qiymatlarni hisoblash 
    p(n,j)=(4.0*p(n-1,j)-p(n-2,j))/3;  
    p(1,j)=(4.0*p(2,j)-p(3,j))/3;          
end        

for i=1:n   % keyingi qatlam uchun boshlangich qiymatni hisoblash 
    for j=1:n      
        p0(i,j)=p(i,j);  
    end  
end       
end

function [p0,p] = fyx(n,tau,h,p0,x,y,t,jt)
% k+1 vaqt qatlamida hisoblash
for i=2:n-1    % Tenglamalar koeffitsientini hisoblash 
    for j=2:n-1  
        %chekli ayirma tenglama koeffitsentlarini hisoblash       
        a(j)=1;
        c(j)=1;
        b(j)=2+2*h*h/tau;
        ff=h*h*(-2*(2*t(jt)*t(jt)*(x(i)*x(i)+y(j)*y(j))+x(i)*y(j))*exp(-2*x(i)*y(j)*t(jt)));   
        d(j)=2*h*h/tau*p0(i,j)+(p0(i-1,j)-2*p0(i,j)+p0(i+1,j))+ff; 
    end
    %Pragonka koeffitsentlarini hisoblash 
    aa1(1)=0; bb1(1)=1;  
    for j=2:n-1 
        aa1(j)=c(j)/(b(j)-aa1(j-1)*a(j));
        bb1(j)=(d(j)+bb1(j-1)*a(j))/(b(j)-aa1(j-1)*a(j));
    end
    % bosim funktsiyasini hisoblash   
    p(i,n)=exp(-2*x(i)*t(jt));  
    for j=n-1:-1:1 
        p(i,j)=aa1(j)*p(i,j+1)+bb1(j);
    end    
end  %i             

for j=1:n  % Chegaraviy qiymatlarni hisoblash 
    p(n,j)=(4.0*p(n-1,j)-p(n-2,j))/3;  
    p(1,j)=(4.0*p(2,j)-p(3,j))/3;          
end        

for i=1:n   % keyingi qatlam uchun boshlangich qiymatni hisoblash 
    for j=1:n      
        p0(i,j)=p(i,j);  
    end  
end       

% k+0.5 vaqt qatlamida hisoblash
for j=2:n-1     % Tenglamalar koeffitsientini hisoblash 
    for i=2:n-1  
        %chekli ayirma tenglama koeffitsentlarini hisoblash  
        a(i)=1;
        c(i)=1;
        b(i)=2+2*h*h/tau;
        ff=h*h*(-2*(2*t(jt)*t(jt)*(x(i)*x(i)+y(j)*y(j))+x(i)*y(j))*exp(-2*x(i)*y(j)*t(jt)));   
        d(i)=2*h*h/tau*p0(i,j)+(p0(i,j-1)-2*p0(i,j)+p0(i,j+1))+ff;  
    end
    %Pragonka koeffitsentlarini hisoblash 
    aa1(1)=0; bb1(1)=1;    
    for i=2:n-1
        aa1(i)=c(i)/(b(i)-aa1(i-1)*a(i));
        bb1(i)=(d(i)+bb1(i-1)*a(i))/(b(i)-aa1(i-1)*a(i));
    end
    % bosim funktsiyasini hisoblash   
    p(n,j)=exp(-2*y(j)*t(jt));  
    for i=n-1:-1:1 
        p(i,j)=aa1(i)*p(i+1,j)+bb1(i);
    end                   
end %j    

for i=1:n % Chegaraviy qiymatlarni hisoblash 
    p(i,n)=(4.0*p(i,n-1)-p(i,n-2))/3;
    p(i,1)=(4.0*p(i,2)-p(i,3))/3;
end      

for j=1:n  % k+1 qatlam uchun boshlangich qiymatni hisoblash  
    for i=1:n      
        p0(i,j)=p(i,j);  
    end  
end         
end





The graph should look like this

Answer 1

[Walter Roberson]

    px(j)=p(21,j); 

You do not define p anywhere in your script before that point.

You do define p strictly inside the functions fxy and fyx, and those functions offer to return p to the calling script or function. However, your calling script has

    for jt=1:nt/2    % Vaqt bo`yicha tsikl}          
    
    fxy(n,tau,h,p0,x,y,t,jt);
    fyx(n,tau,h,p0,x,y,t,jt);
end % jt

That code repeatedly calls the functions fxy and fxy and discards all of their outputs, not saving any of the calculated p0 or p values.

The p0 and p values that the functions offer to return are 2 dimensional arrays. You are calling the functions repeatedly, so you really should be saving the 2 dimensional arrays for each jt value -- so if you decide to store the returned p0 and p then you really should use a 3D array; it looks to me as if you should be using n x n x floor(nt/2) as the output size if you decide to save the returned values.

Then when you get to the loop below that,

for j=1:n
    px(j)=p(21,j); 
    pxt(j)=pt(21,j);
end                 

if you have saved the return values from the functions, then is that p intended to refer to the return value from fxy? Is it intended to refer to the return value from fyx? Which particular value of jt is it intending to be using when you pull out the values in that for j loop ?

meshc(x,y,p) %Uch o'lchovli 3D grafika

if you have saved the return values from the functions, then is that p intended to refer to the return value from fxy? Is it intended to refer to the return value from fyx? Which particular value of jt is it intending to be using when you meshc() ? You cannot use them all because you (should have) saved a 3D array for p, one n x n array for each for jt value, and when you call meshc(), the third parameter needs to be a 2d array, not a 3d array.

contour(x,y,p,'ShowText','on','LineWidth',2); %kontur chizish 

if you have saved the return values from the functions, then is that p intended to refer to the return value from fxy? Is it intended to refer to the return value from fyx? Which particular value of jt is it intending to be using when you contour() ? You cannot use them all because you (should have) saved a 3D array for p, one n x n array for each for jt value, and when you call contour(), the third parameter needs to be a 2d array, not a 3d array.

[Shikhnazar Ismailov]

Were both functions used in the correct order?

[Walter Roberson]

The functions appear to be independent of each other, so the order only matters if you are overwriting variables.

[Shikhnazar Ismailov]

The second function takes the values of p and p0 derived from the first function. The first function takes the values of p and p0 derived from the second function. Only in the beginning does the first function work with the above values of p and p0, otherwise it must calculate the mutual exchange. How can I do this?

[Walter Roberson]

As I said before, record the output of the fxy call. Then, if appropriate, pass that output into fyx in the appropriate position in the calling sequence.

[Shikhnazar Ismailov]

If the loop rotates, the fyx value is used in fxy, how can I send it to fxy?

[Walter Roberson]

Generally speaking, code sometimes has this kind of structure

initial_value_of_variable = (some constant)
initial_value_of_something_else = (some other constant)

current_value_of_variable = initial_value_of_variable;
current_value_of_other_variable = initial_value_of_something_else

start a loop
   some_variable = some_function(current_value_of_variable, current_value_of_other_variable);
   some_other_variable = some_other_function(some_variable, current_value_of_other_variable);
   
   current_value_of_variable = some_variable;
   current_value_of_other_variable = some_other_variable;
 end of loop

That is, you initialize some variables first, and then you refine the values inside the loop, and then set the refined value as being the "current" value that will become the input for the next cycle of the loop.