Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/16172
Title: A uniformly convergent numerical scheme for singularly perturbed non-linear eigenvalue problem under constraints
Authors: CHAI MING HUANG
Keywords: Bose-Einstein Condensation, Gross-Pitaevskii equation, semiclassical regime, adaptive mesh scheme, ground state, excited states.
Issue Date: 17-Apr-2007
Source: CHAI MING HUANG (2007-04-17). A uniformly convergent numerical scheme for singularly perturbed non-linear eigenvalue problem under constraints. ScholarBank@NUS Repository.
Abstract: We present a uniformly convergent numerical scheme to solve the singularly perturbed nonlinear eigenvalue problem --- the time-independent Gross-Pitaevskii equation in the semiclassical regime, which is used to describe the equilibrium properties of Bose-Einstein Condensate at extremely low temperature. The numerical scheme proposed is based on the piecewise uniform mesh. Through detailed numerical error analysis, the numerical scheme presented is found to be uniformly convergent and is able to treat the interior layers or boundary layers inherent in the solutions of the singularly perturbed nonlinear eigenvalue problem. A comparison of this new numerical scheme based on the piecewise uniform mesh is made against the classical numerical scheme based on uniform mesh and we found that the numerical accuracy is greatly enhanced with the new scheme. We also extended the new numerical scheme to two dimensions and applied it to solve the singular perturbed nonlinear eigenvalue problem in two dimensions.
URI: http://scholarbank.nus.edu.sg/handle/10635/16172
Appears in Collections:Master's Theses (Open)

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