A priori error analysis of linear and nonlinear periodic Schrödinger equations with analytic potentials

DOI10.1007/s10915-023-02421-0arXiv2206.04954OpenAlexW4281674850MaRDI QIDQ6178633

Eric Cancès, Antoine Levitt, Gaspard Kemlin

Publication date: 16 January 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2206.04954

zbMATH Keywords

Schrödinger equationeigenvalue problemsdiscretization errornumerical analysisanalytical potentialsplanewave discretization

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Eigenvalue problems for linear operators (47A75) Analyticity in context of PDEs (35A20) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Computational density functional analysis in statistical mechanics (82M36)

Cites Work

• Numerical analysis of nonlinear eigenvalue problems
• On the limited memory BFGS method for large scale optimization
• Duffing-type oscillator with a bounded from above potential in the presence of saddle-center bifurcation and singular perturbation: frequency control
• A remark on the analyticity of the solutions for nonlinear elliptic partial differential equations
• Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models
• On the Analyticity of the Solutions of Analytic Non-Linear Elliptic Systems of Partial Differential Equations: Part I. Analyticity in the Interior
• A Simplification of the Hartree-Fock Method
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