#finite difference method

Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50042 DOI: 10.4236/jemaa.2014.610031 Author(s) Serigne Bira Gueye, Kharouna Talla, Cheikh Mbow 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. eww141009gjr 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. KEYWORDS 1D Poisson Equation, Finite Difference Method, Neumann-Dirichlet, Dirichlet-Neumann, Boundary Problem, Tridiagonal Matrix Inversion, Thomas Algorithm

Read the full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50041 DOI: 10.4236/jemaa.2014.610030 Author(s) Serigne Bira Gueye 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. EWW141007GJR This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena. KEYWORDS 1D Poisson Equation, Finite Difference Method, Tridiagonal Matrix Inversion, Thomas Algorithm, Gaussian Elimination, Potential Problem