Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity

DOI10.1016/j.cam.2022.114632zbMath1502.65107OpenAlexW4288459455WikidataQ113878683 ScholiaQ113878683MaRDI QIDQ2088800

Yvonne Bronsard Alama

Publication date: 6 October 2022

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2022.114632

zbMATH Keywords

error estimatesnonlinear Schrödinger equationnumerical analysislow regularitystability and convergence of numerical methodsanalysis of nonlinear PDEs

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)

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Numerical Integration of Schrödinger Maps via the Hasimoto Transform ⋮ Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schrödinger Equation with Low Regularity Potential and Nonlinearity

Cites Work

• Error bounds for exponential operator splittings
• Low regularity exponential-type integrators for semilinear Schrödinger equations
• KIOPS: a fast adaptive Krylov subspace solver for exponential integrators
• Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity
• An exponential-type integrator for the KdV equation
• Exponential integrators
• Fourier Analysis and Nonlinear Partial Differential Equations
• On Commutators of Singular Integrals and Bilinear Singular Integrals
• Trigonometric time integrators for the Zakharov system
• A General Framework of Low Regularity Integrators
• Resonance-based schemes for dispersive equations via decorated trees
• Crank–Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
• Geometric Numerical Integration