neuman boundary condtions (no flux) from interior points

Hello,

i hope someone can give me a hint. Or better a solution. But i am glad about any help.

I would like to solve an advection diffusion equation with d03pf. It is somehow working, but i don`t understand how to set no flux boundaries. Therfore my results are physically not correct. As the solution for the first three interior points is given i could simply say u(1)=u(2) and u(end)=u(end-1) this i get from a backward difference with zero as solution. But either my solution is constant over the whole domain, or a wave flowing in my domain.

In other words the mass in my system is conserved. Nothing flowing out, nothing flowing in everything is settling by gravity. In pdepe or d03pc it is simple because i just have to set pl ans pr to 1. But here i do have to set the boundary with the solution in the boundary region, time and x(1D space variable).

Should i calculate my flux term and my corresponding diffusion term at the boundary and set the sum to zero? Just extrapolating my solution and set it to zero ? Backward Euler of the solution and set that to zero ? Or are there known methods in order to do that ?

Any help would be appreciated