A Uniformly Convergent Numerical Method for Singularly Perturbed Nonlinear Eigenvalue Problems

作     者：Weizhu Bao Ming-Huang Chai 

作者机构：Department of Mathematics and Center for Computational Science and EngineeringNational University of Singapore117543Singapore Department of MathematicsNational University of Singapore117543Singapore. NUS High SchoolNational University of Singapore117543Singapore. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2008年第4卷第6期

页      面：135-160页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Singapore Ministry of Education grant No.R-146-000-083-112 and would like to thank Professor Tao Tang for very helpful discussion on the subject 

主　　题：Nonlinear eigenvalue problem Bose-Einstein condensation ground state excited state energy chemical potential piecewise uniform mesh. 

摘      要：In this paper we propose a uniformly convergent numerical method for discretizing singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation and quantum *** begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly perturbed nonlinear eigenvalue problem under a *** asymptotic approximations for the problem are presented to locate the positions and characterize the widths of boundary layers and/or interior layers in the solution.A uniformly convergent numerical method is proposed by using the normalized gradient flow and piecewise uniform mesh techniques based on the asymptotic approximations for the *** numerical results are reported to demonstrate the effectiveness of our numerical method for the ***,the method is applied to compute ground and excited states of Bose-Einstein condensation in the semiclassical regime and some conclusive findings are reported.