Good day,

I am having a bit a trouble solving this system:

Incorporating the following central difference approximations:

I've made an attempt to solve this using a method I use when I encounter linear de's rather than a system. I don't know if its valid in a system case...

First thing, I shifted the indices for

ie.

Substituting these into the

:

Where,

From here I let

, sub it into the equation and basically solve for n.

I get a solution for

that contains like 6 constants.

I use this to solve for

which results in a long solution with many square roots.

As I mentioned I'm highly doubtful if this is actually how you do it... Any help would be greatly appreciated.

Thanks