1D diffusion equation using Matlab

clear all
close all
clc

%%Defining the Mesh

n_points = 5 ; % Total number of points
dom_size = 1;  % Size of the Domain
h = dom_size/(n_points - 1); % Space between each grid

% Initializing the Problem

y(1) = 0;
y(n_points) = 1;

y_new(1) = 0;
y_new(n_points) = 1;

error_mag = 1;
error_req = 1e-7;
iterations = 0;
 
%%Calculations

while error_mag > error_req
    for i = 2:(n_points - 1);
        y_new(i) = 0.5 .*(y(i-1) + y(i+1));
        iterations = iterations +1;
    end
    
    % calculation of error magnitude
    error_mag = 0;
    for i = 2:(n_points - 1)
        error_mag = error_mag + abs(y(i) - y_new(i));
    end
    
    % Assigning new to the old
    y = y_new;
end

%Plotting

x_dom = ((1:n_points)-1).*h;
figure;
plot(x_dom,y)