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

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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

Accepted Answer

Torsten
Torsten on 23 Nov 2022
Change
dx = 1.01/(Nx-1);
dy = 1.01/(Ny-1);
to
dx = 1.0/(Nx-1);
dy = 1.0/(Ny-1);
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More Answers (1)

Voss
Voss on 23 Nov 2022
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

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