TITLE:
The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method
AUTHORS:
Serigne Bira Gueye
KEYWORDS:
1D Poisson Equation, Finite Difference Method, Tridiagonal Matrix Inversion, Thomas Algorithm, Gaussian Elimination, Potential Problem
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.6 No.10,
September
25,
2014
ABSTRACT: A new
method for solving the 1D Poisson equation is presented using the finite
difference method. This method is based on the exact formulation of the inverse
of the tridiagonal matrix associated with the Laplacian. This is the first time
that the inverse of this remarkable matrix is determined directly and exactly.
Thus, solving 1D Poisson equation becomes very accurate and extremely fast.
This method is a very important tool for physics and engineering where the
Poisson equation appears very often in the description of certain phenomena.