Generalization of the Exact Solution of 1D Poisson Equation with Robin Boundary Conditions, Using the Finite Difference Method
Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=50586#.VEX3BVfHRK0 Author(s) Serigne Bira Gueye , Kharouna Talla , Cheikh Mbow Affiliation(s) Département de Physique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar-Fann, Sénégal . 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 ( h 2 )), and very fast ( O ( N ...