Two-grid discretization methods for nonlinear Schrödinger-Poisson system

• Main Authors: Chin-Yi Lin, 林進一
• Other Authors: Cheng-Sheng Chien
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/38288700889616762369

碩士 === 國立中興大學 === 應用數學系 === 93 === We present a new implementation of the two-grid centered difference method for computing extremum eigenpairs of self-adjoint partial differential operators with periodic boundary conditions, which in general possess multiple and clustered eigenvalues. One typical example is the Schrödinger eigenvalue problem. Based on this method we develop a novel two-grid centered difference method for the numerical solutions of the nonlinear Schrödinger-Poisson eigenvalue problem. Our numerical results show how the first few eigenpairs of the Schrödinger eigenvalue problem are affected by the dopant which is considered in the Schrödinger-Poisson system. Next, we present some variants of the two-grid centered difference discretization schemes for tracing solution branches of semilinear elliptic eigenvalue problems. We mainly perform exact and inexact corrections on the fine grid by considering linear approximations of operator equations. Sample numerical results are reported.