TITLE:
Solution of 1D Poisson Equation with Neumann-Dirichlet and Dirichlet-Neumann Boundary Conditions, Using the Finite Difference Method
AUTHORS:
Serigne Bira Gueye, Kharouna Talla, Cheikh Mbow
KEYWORDS:
1D Poisson Equation, Finite Difference Method, Neumann-Dirichlet, Dirichlet-Neumann, Boundary Problem, Tridiagonal Matrix Inversion, Thomas Algorithm
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.6 No.10,
September
25,
2014
ABSTRACT: An
innovative, extremely fast and accurate method is presented for
Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson
equation, and the diffusion and wave equation in quasi-stationary regime; using
the finite difference method, in one dimensional case. Two novels matrices are
determined allowing a direct and exact formulation of the solution of the
Poisson equation. Verification is also done considering an interesting
potential problem and the sensibility is determined. This new method has an
algorithm complexity of O(N), its truncation error goes like O(h2),
and it is more precise and faster than the Thomas algorithm.