Error plotting with space and time

Hello,

I do not understand how to plot/visualize a solution to some function with different time and space steps. I have the below function handle and I need to plot the exact solution to approximate the the error in the approximate solution. Can someone please explain the most efficient method of doing this? I have not calculted the approximation yet, but it will be in a 2x2 array format, please also elaborate on plotting the error.

%attempt
sigma=12
alpha=0.01
exact = @(t,x) exp(-(x-0.4).^2/(2*alphat + 1/sigma))/sqrt(sigma*alpha*t+3);
Nt=200;dt=1/Nt;
Nx=20;dx=1/Nx;
t1=linspace(0,1,dt)
x1=linspace(0,1,dx)
plot(t1,x1,exact(t1,x1)

% How to approach an error analysis/plot?
%I understand it is the delta detween exact and approx at the points in question
% I just need a cleaner/efficient way of doing this

Answer 1

[Image Analyst]

There are a number of errors there. Not exactly sure what you want, but is this closer?

% attempt
sigma=12
alpha=0.01
exact = @(t,x) exp(-(x-0.4).^2 ./(2*alpha * t + 1/sigma)) ./ sqrt(sigma*alpha.*t+3);
Nt=200;
dt=1/Nt;
Nx=200;
dx=1/Nx;
t1=linspace(0,1,Nt)
x1=linspace(0,1,Nx)
[t2, x2] = meshgrid(t1, x1);
output = exact(t2,x2)
imshow(output, []);
colormap(jet(256));
colorbar;