%% Forward Euler and gradient fields
% 
% Consider the first order ODE $y'(x) = f(x,y)$.
% There is a close relation between the Forward Euler (FE) method and the
% gradient field of the function $f$, due to the way FE discretise.
%
%% The GUI
%
% Running the downloadable MATLAB(R) code on this page opens a GUI which
% demonstrates the relation between FE and gradient fields.
% 
gradient_field_GUI
%% Interface
% 
% You can input the axes limits, the RHS of the ODE equation, the exact
% solution (if known), the time-step $h$, and the initial condition $y(x_0)
% = y_0$. 
%
% By clicking on 'Plot field lines', the field lines of the function $f$
% will appear. You can control the density of the field lines by changing
% the parameter 'Distance field lines'.
%
% To start the animation, click on 'Start animation'. Once the animation
% begins, to stop it click on 'Stop animation'. 
%
% Notice that the exact solution is plotted in red, while the FE
% approximation is plotted in blue. You can see that the numerical error
% makes the FE approximation go to adjacent field lines.
%
%% Code
%
% * <gradient_field_GUI.m> (Run this)
% * <gradient_field_GUI.fig> (Required - GUI figure)
%
% All files as .zip archive: <gradient_field_all.zip>

