The size of X must match the size of Z or the number of columns of Z.

I am trying to solve the 2d laplace equation for heat conduction using forward diffrence scheme, but I'm getting an error:The size of X must match the size of Z or the number of columns of Z in line 92. here's my code:

clear all
close all
clc
% % geometry of domain
Nx = 102;
Ny = 102;
dx = 1.01/(Nx-1);
dy = 1.01/(Ny-1);
X = 0:dx:1;
Y = 0:dy:1;
% % initial condition
T = zeros(Nx,Ny);
T(50,20) = 2.5;
T(25,25) = -0.5;
T(75,10) = -2.5;
% % boundary condition
TL = 1;
TR = cos(6*(3*pi*Y)/2)+1;
TT = 1;
TB = 1+X;
T(:,1) = TL;
T(Ny,:) = TT;
T(:,Nx) = TR(Nx-1);
T(1,:) = TB(1);
T(:,2) = TL;
T(Ny-1,:) = TT;
T(2,:) = TB(2);
T(:,Nx-1) = TR(Nx-2);
T_new(Nx,Ny) = 0;
TL = 1;
TR = cos(6*(3*pi*Y)/2)+1;
TT = 1;
TB = 1+X;
T_new(:,1) = TL;
T_new(Ny,:) = TT;
T_new(:,Nx) = TR(Nx-1);
T_new(1,:) = TB(1);
T_new(:,2) = TL;
T_new(Ny-1,:) = TT;
T_new(2,:) = TB(2);
T_new(:,Nx-1) = TR(Nx-2);
error_mag = 5;
error_req = 1e-07;
iteration = 0;
% % calculation
while error_mag > error_req
    for i = 2:Nx-2
        for j=2:Ny-2
            T_new(i,j) = (2*T(i+1,j)-T(i+2,j)+2*T(i,j+1)-T(i,j+2))/2; % forward difference scheme
            T_new(50,20) = 2.5;
            T_new(25,25) = -0.5;
            T_new(75,10) = -2.5;
            TL = 1;
            TR = cos(6*(3*pi*Y)/2)+1;
            TT = 1;
            TB = 1+X;
            T_new(:,1) = TL;
            T_new(Ny,:) = TT;
            T_new(:,Nx) = TR(Nx-1);
            T_new(1,:) = TB(1);
            T_new(:,2) = TL;
            T_new(Ny-1,:) = TT;
            T_new(2,:) = TB(2);
            T_new(:,Nx-1) = TR(Nx-2);
            iteration = iteration +1;
        end
    end
    % calculation of error magnitude
    
    for i= 2:Nx-2
        for j = 2:Ny-2
            error_mag =  abs(T(i,j)-T_new(i,j));
            
        end
    end
    %assigning new to old
    T = T_new;
end
% % plotting
[x,y] = meshgrid(X,Y);
colormap("jet");
contourf(X,Y,T');
colorbar

Answer 1

[Abhaya]

Hi Kushagra,

I understand you are trying to solve the 2d Laplace equation for heat conduction using forward difference scheme, but getting the error that “The size of X must match the size of Z or the number of columns of Z”. This issue arises because the vectors X and Y have a size of 101, whereas the matrix T has a size of 102x102. When you use MATLAB ‘contourf’ function with the parameters‘X’,‘Y’, and‘Z’, the‘Z’parameter represents the height or value at the corresponding(X, Y)location. So the size of vector ‘X’ must match with column size of matrix ‘T`’.

A possible workaround is to extend the vector ‘X’ and vector ‘Y’ up to 1.01 with increment of ‘dx’ and ‘dy’ respectively. This will result vectors ‘X’ and ‘Y’ each of size 102.

Another workaround is to create a 'meshgrid' of 102x102 by appending 0 to the beginning of the vectors 'X' and 'Y'.

% % plotting
X1=[0 X];
Y1=[0 Y];
[x,y] = meshgrid(X1,Y1);
colormap("jet");
contourf(x,y,T');
colorbar

For further explanation follow the documentation of MATLAB ‘contourf’ function.

https://www.mathworks.com/help/matlab/ref/contourf.html

Hope this helps.

[Kushagra Saurabh]

Thank you Abhaya