We present an analytical solution to the generalized discrete Poisson equation, a matrix equation which has a tridiagonal matrix with fringes having an arbitrary value for the diagonal elements. The results are of relevance to a variety of physical problems, which require the numerical solution of the Poisson equation. As examples, the formula has been applied to the solution of the electrostatic problem of tunnelling junction arrays with two and three rows.
Publication Source (Journal or Book title)
Journal of Physics A: Mathematical and General
Hu, G., Ryu, J., & O'Connell, R. (1998). Analytical solution of the generalized discrete Poisson equation. Journal of Physics A: Mathematical and General, 31 (46), 9279-9282. https://doi.org/10.1088/0305-4470/31/46/017