% Integrate the general problem du/dt = Au forward in time
% using a 2nd order Adams-Bashforth integration given:
%
% dt: timestep
% Tf: final time
% uinit: initial vector
%
% The numerical approximation is placed in the vector v
%

% Set initial condition into v
v(:,1) = uinit;
n = 1;
t(1) = 0;

% Integrate first step using Forward Euler
v(:,n+1) = v(:,n) + dt*A*v(:,n);
t(n+1) = t(n) + dt;
n = n + 1;

% Integrate remaining steps using AB2
while (t(n) < Tf),
  v(:,n+1) = v(:,n) + dt*A*(1.5*v(:,n) - 0.5*v(:,n-1));
  t(n+1) = t(n) + dt;
  n = n + 1;
end