TITLE:
Generalization of the Exact Solution of 1D Poisson Equation with Robin Boundary Conditions, Using the Finite Difference Method
AUTHORS:
Serigne Bira Gueye, Kharouna Talla, Cheikh Mbow
KEYWORDS:
Robin Boundary, Poisson Equation, Matrix Inversion
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.6 No.12,
October
17,
2014
ABSTRACT: A new and
innovative method for solving the 1D Poisson Equation is presented, using the
finite differences method, with Robin Boundary conditions. The exact formula of
the inverse of the discretization matrix is determined. This is the first time
that this famous matrix is inverted explicitly, without using the right hand
side. Thus, the solution is determined in a direct, very accurate (O(h2)),
and very fast (O(N)) manner. This new approach treats all cases of boundary
conditions: Dirichlet, Neumann, and mixed. Therefore, it can serve as a
reference for solving the Poisson equation in one dimension.