The Lattice Green Function for the Poisson Equation on an Infinite Square Lattice

Details The Lattice Green Function for the Poisson Equation on an Infinite Square Lattice The Lattice Green Function for the Poisson Equation on an Infinite Square Lattice

2005-08-31

arxiv.org/abs/cond-mat/0509002v1

Physics

Condensed Matter

Other Condensed Matter

6 pages, LaTeX created with LyX 1.3.5. For associated Maxima code see http://www.exstrom.com/lgf/lgf.html

Scientific paper

We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first order difference equations, which can then be solved sequentially. These formulas are useful in solving two dimensional Poisson equation problems using the finite difference approximation.

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