Can you suggest any method for stability analysis of FTCS scheme for the the following parabolic equation ?
D.E: $u_{t}=a(x,t)u_{xx}+f(x,t,u)$, $0<x<1$, $0<t<T$, $T>0$
BCs: $u_{x}(0,t)+hu(0,t)=0$, $u(1,t)=0$
IC: $u(x,0)=g(x)$
I consider the von neumann method but it requires that the coefficient must be constant and as far as I know it does not use boundary condition. Can you find stability condition in Lax-Ricthmeyer sense?
Thanks in advance...