MATLAB: How to nondimensionalized plot axis

nondimensionalize

clc
clear all
%set number of nodes
Nx=51; % x nodes
Ny=51; % y nodes
%define constants
a=1; %normalized x length
b=1; %normalized y length
H=1; %H is a constant
%grid spacing
dx=a/(Nx-1); %grid spacing in x direction
dy=b/(Ny-1); %grid spacing in y direction
%build grid
x=dx*(0:(Nx-1)); %points along x
y=dy*(0:(Ny-1)); %points along y
[X,Y]=meshgrid(x,y);
%initialize theta
theta=zeros(Nx,Ny); %initialize theta to zero
%Left Boundary Condition
theta(1,:)=y.*(1-y);
%begin iteration (jacobi)
for n=1:100000 %number of iterations
    I=2:(Nx-1);
    J=2:(Ny-1);
%update the interior points
theta(I,J)=(dy^2*(theta(I+1,J)+theta(I-1,J))+...
    (a*dx/b)^2*(theta(I,J+1)+theta(I,J-1)))/(2*dy^2+2*(a*dx/b)^2);
%update top boundary
theta(I,Ny)=(4*theta(I,Ny-1)-theta(I,Ny-2))/(3+2*dy*H);
%update right boundary
theta(Nx,J)=(4*theta(Nx-1,J)-theta(Nx-2,J))/3;
%corner points (average above and below)
theta(1,1)=(theta(1,2)+theta(2,1))/2;
theta(1,Ny)=(theta(1,Ny-1)+theta(2,Ny))/2;
theta(Nx,Ny)=(theta(Nx-1,Ny)+theta(Nx,Ny-1))/2;
theta(Nx,1)=(theta(Nx-1,1)+theta(Nx,2))/2;
end
flipud(theta')%this is important because this reverses the rows and cols to match x and y
%plots
figure
plot(theta(:,(Ny+1)/2));
title('theta(X,0.5) vs X')
xlabel('X')
ylabel('theta(0.5,Y)')
figure
plot(theta((Nx+1)/2,:));
title('theta(0.5,Y) vs Y')
xlabel('Y')
ylabel('theta(0.5,Y)')
figure
contourf(X,Y, theta');
title('theta(X,Y)')
xlabel('X')
ylabel('Y')
Outputs 3 figures. I want the horizontal axis on the line graphs to read from 0 to 1. Can anyone please help? Thanks

Best Answer

plot(X, theta(:,(Ny+1)/2));
plot(X, theta((Nx+1)/2,:));
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