function [t, u] = rk4(dudt, tspan, u0, n)
% RK4    Fourth-order Runge-Kutta for an IVP.
%
% Input:
%   dudt    defines f in u'(t)=f(t,u)  (function)
%   tspan   endpoints of time interval (2-vector)
%   u0      initial value (vector, length m)
%   n       number of time steps (integer)
%
% Output:
%   t       selected nodes (vector, length n+1)
%   u       solution values (array, (n+1) by m)

    % Define time discretization.
    a = tspan(1);  
    b = tspan(2);
    h = (b-a)/n;
    t = a + (0:n)'*h;
    
    % Initialize solution array.
    u = zeros(length(u0), n+1);
    u(:,1) = u0(:);
    
    % Time stepping.
    for i = 1:n
      k1 = h*dudt( t(i),     u(:,i) );
      k2 = h*dudt( t(i)+h/2, u(:,i)+k1/2 );
      k3 = h*dudt( t(i)+h/2, u(:,i)+k2/2 );
      k4 = h*dudt( t(i)+h,   u(:,i)+k3 );
      u(:,i+1) = u(:,i) + (k1 + 2*(k2 + k3) + k4)/6;
    end
    
    u = u.';   % conform to MATLAB output convention
end