Multilevel Spectral-Galerkin and Continuation Methods for Nonlinear Schrödinger Equations

DOI10.1137/090749177zbMath1191.65132OpenAlexW1982636567MaRDI QIDQ3567036

Huei-Shuang Chen, Cheng-Sheng Chien

Publication date: 10 June 2010

Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/090749177

zbMATH Keywords

algorithmnumerical resultsnonlinear Schrödinger equationperiodic potentialBose-Einstein condensationenergy levelmultilevel spectral-Galerkin continuation methods

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Spectral collocation and a two-level continuation scheme for dipolar Bose-Einstein condensates ⋮ Unconditional optimal error estimates of a linearized mass- and energy-conservation FEM for a coupled nonlinear Schrödinger equations ⋮ A spectral-Galerkin continuation method using Chebyshev polynomials for the numerical solutions of the Gross-Pitaevskii equation ⋮ Spectral collocation methods using sine functions for a rotating Bose-Einstein condensation in optical lattices ⋮ Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D ⋮ Pseudospectral Methods for Computing the Multiple Solutions of the Schrodinger Equation ⋮ A spectral-Galerkin continuation method for numerical solutions of the Gross-Pitaevskii equation ⋮ Efficient spectral collocation and continuation methods for symmetry-breaking solutions of rotating Bose–Einstein condensates ⋮ MIXED FOURIER-LEGENDRE SPECTRAL METHODS FOR THE MULTIPLE SOLUTIONS OF THE SCHRODINGER EQUATION ON THE UNIT DISK

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