Error plotting with space and time

3 views (last 30 days)
jojo
jojo on 17 May 2020
Answered: Image Analyst on 17 May 2020
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

Answers (1)

Image Analyst
Image Analyst on 17 May 2020
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;

Categories

Find more on Vector Fields in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!