Please help on solving these complex equations

Please help on solving these difficult equations

In the pdf document I attached there are equations numbered (12) ,(13), (14).
These are similar equations.
I want to find a way to iteratively solve the equation number (13).
I was told that this equation can be rearranged to the form, "Ax=B".
Please help me on re-arranging the terms of this equation to this form.

Thank you.
 

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HallsofIvy

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You want to solve equation 13 for WHAT variable?
 
I want to solve these equation 13 for variable "n". Here n[j] is the electron density in the i,j position at time "t+1".

So the matrix "x" (if this can be rearranged to the form Ax=B) should contain the values of "n" at the positions (i,j),(i,j-1),(i,j+1),(i-1,j),(i+1,j).

matrix "B" would contain the all the constant terms at time "t".(D(E,x), R(n,p) & n[t]).

Thank you
 
Can somebody convert equation 13 into the matrix form.
i.e Ax=B
 

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