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
Substituting these into the :
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.