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

i'am trying to solve 2d laplace equation using fourth order central difference could but i'am getting an error:The size of X must match the size of Z or the number of columns of Z, During plotting. could someone help me here.

My code is:

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-1);
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-1);
error_mag = 3;
error_req = 1e-03;
iteration = 0;
% % calculation
while error_mag > error_req
    for i = 3:Nx-2
        for j=3:Ny-2
            T_new(i,j) = (16*T(i+1,j)+16*T(i-1,j)-T(i-2,j)-T(i+2,j)-T(i,j+2)+16*T(i,j+1)+16*T(i,j-1)-T(i,j-2))/60; % fourth order central difference
            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-1);
            iteration = iteration +1;
        end
    end
    % calculation of error magnitude
    
    for i= 3:Nx-2
        for j = 3: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');

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

colorbar

Answer 1

[Torsten]

Change

dx = 1.01/(Nx-1);
dy = 1.01/(Ny-1);

to

dx = 1.0/(Nx-1);
dy = 1.0/(Ny-1);

[Kushagra Saurabh]

Then what will happen to initial conditions i.e. T(50, 20) = 2.5 and so on?

[Torsten]

Your settings are inconsistent.

Either change

dx = 1.01/(Nx-1);
dy = 1.01/(Ny-1);

to

dx = 1.0/(Nx-1);
dy = 1.0/(Ny-1);

or change

X = 0:dx:1;
Y = 0:dy:1;

to

X = 0:dx:1.01;
Y = 0:dy:1.01;

In either case,

T(ix,iy) will be T at P=((ix-1)*dx,(iy-1)*dy)

[Kushagra Saurabh]

I got the plot using your 1st suggestion but i 'm not getting my right boundary condition into it, could you please check..

[Torsten]

What do you mean by "i 'm not getting my right boundary condition into it" ? And where can I check ?

For (i = 2 and i = Nx-1) and (j = 2 and j = Ny-1), you will have to do the standard discretization with the second-order central difference star. You should replace the boundary conditions settings for these points since they are no boundary points.

[Kushagra Saurabh]

[Kushagra Saurabh]

I'm getting this profile but is it correct? for fourth corder central difference scheme for 2d laplace equation and I'm not seeing my right boundary condition :T_new(:,Nx-1) = TR(Nx-1) here in the plot..

[Torsten]

Didn't you read my comment ?

For (i = 2 and i = Nx-1) and (j = 2 and j = Ny-1), you will have to do the standard discretization with the second-order central difference star. You must replace the boundary conditions settings for these points since they are no boundary points.

[Kushagra Saurabh]

sorry sir, but i didn't get you.. actually, i don't know how to put as you said.

[Torsten]

T_new(i,j) = (T(i+1,j)+T(i-1,j)+T(i,j+1)+T(i,j-1))/4; % second order central difference

for i = 2, 2 <= j <= Ny-1

for j = 2, 2 <= i <= Nx-1

for i = Nx-1, 2<=j <= Ny-1

for j = Ny-1, 2<= i <= Nx-1

[Kushagra Saurabh]

Thank you so much..

Answer 2

[Voss]

The error happens because T is a 102-by-102 matrix but X and Y only have 101 elements:

% % 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);

whos X Y T

  Name        Size             Bytes  Class     Attributes

  T         102x102            83232  double              
  X           1x101              808  double              
  Y           1x101              808  double