Reaction diffusion equation script

I need to build a generic script for solving a reaction-diffusion equation of the form-

du/dx = f(u) +D(du/dx)^2

that is based on the explicit Euler method. I have to include the possibility of choosing different boundary conditions.

I have no idea what to do from this point.

The code I have for the Euler method is-

function [U] = Euler(f,y,dt,tmax)

%func - is a function handle
%dt - the steps
%tmax - the maximal time
%y - the first guess
t = dt:dt:tmax; 
n = length(t);
U = zeros(length(y),n); 
U(:,1) = y;

U_old = y(:);

for i=1:length(t)-1
    U_new = U_old+dt.*f(t(i),U_old);
    U(:,i+1)=U_new;
    U_old=U_new;
end

% grid on; 
% plot3(U(1,:),U(2,:),U(3,:),'-b','linewidth');
% title('Solution with Eulers method','fontsize',15);
% xlabel('x','fontsize',18); ylabel('y','fontsize',18); zlabel('z','fontsize',18);
end

[Torsten]

You mean

du/dx = f(u) +D(du/dx)^2

or

du/dt = f(u) +D(du/dx)^2

?

[Irit Amelchenko]

I meant du/dt = f(u) +D(du/dx)^2

Can't edit the question.

[Torsten]

And you really mean (du/dx)^2 and not d^2u/dx^2 ?