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The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

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.


Auteur(s) : Gueye Serigne Bira
Pages : 303-308
Année de publication : 2014
Revue : Journal of Electromagnetic Analysis and Applications (JEMAA)
N° de volume : 6
Type : Article
Mise en ligne par : GUEYE Serigne Bira