Gueye, S.B., Talla, K. and Mbow, C. (2014) Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method. Journal of Electromagnetic Analysis and Applications, 6, 309-318.
http://dx.doi.org/10.4236/jemaa.2014.610031

has been cited by the following article:

• 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.