How does this Euler's Method for first ODE work?

1 -  function [x,y] = Euler(h, x0, y0, interval_length, func)
2 -  nsteps = floor(interval_length/h) + 1;
3 -  x = zeros(nsteps,1);
4 -  y = zeros(nsteps,1);
5-  x(1) = x0;
6-  y(1) = y0;
7 -  for i=2:nsteps
8 -     y(i) = y(i-1) + h* func(x(i-1), y(i-1));
9 -     x(i) = x(i-1) + h;
10 - end

Please explain how this program works line by line I am trying to understand it so I can learn how to use it properly.

Answer 1

[darova]

Here are some basic concepts

1 -  function [x,y] = Euler(h, x0, y0, interval_length, func)
% h - step in X direction (dx)
% x0 - initial position (start value)
% y0 - initial position (start value)
% interval_length - how far object will move from x0
% func - derivate function of y (dy/dx == y' == f(x,y))
2 -  nsteps = floor(interval_length/h) + 1;                    % number of points (steps)
3 -  x = zeros(nsteps,1);                                      % preallocation (memory reserving for array)
4 -  y = zeros(nsteps,1);                                      % preallocation (memory reserving for array)
5-  x(1) = x0;                                                 % initialization of array
6-  y(1) = y0;                                                 % initialization of array
7 -  for i=2:nsteps                                            % for loop. Everything between FOR .. LOOP is repeated
8 -     y(i) = y(i-1) + h* func(x(i-1), y(i-1));               % increase Y position
9 -     x(i) = x(i-1) + h;                                     % increase X position
10 - end

Google more about Euler Method