I have the next PDE system:
$u_t=D_u u_{xx}-u+av+u^2v\\ v_t=D_v v_{xx}+b-av-u^2v$
Where $D_u,D_v,a,b$ are constants. I want to build or find a implicit SECOND ORDER scheme for this PDE system. I have and explicit scheme already builded but it is so unstable, and I know that implicit scheme are unconditionally stable.
How can I find/build a second order implicit scheme?