A novel, structure-preserving, second-order-in-time relaxation scheme for Schrödinger-Poisson...

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A conservative relaxation Crank-Nicolson finite element method for the Schr\"{o} dinger-Poisson equation

H Liu, N Yi, P Yin - arXiv preprint arXiv:2405.12848, 2024 - arxiv.org
In this paper, we propose a novel mass and energy conservative relaxation Crank-Nicolson
finite element method for the Schr\"{o} dinger-Poisson equation. Utilizing only a single …
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[PDF] arxiv.org

Efficient numerical approximations for a non-conservative Nonlinear Schrodinger equation appearing in wind-forced ocean waves

A Athanassoulis, T Katsaounis, I Kyza - arXiv preprint arXiv:2401.16835, 2024 - arxiv.org
We consider a non-conservative nonlinear Schrodinger equation (NCNLS) with time-
dependent coefficients, inspired by a water waves problem. This problem does not have …
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Unconditionally convergence and superconvergence error analysis of a mass-and energy-conserved finite element method for the Schrödinger–Poisson equation

H Yang, X Liu - Computational and Applied Mathematics, 2024 - Springer
This paper aims to investigate the unconditionally optimal and superconvergent error
estimates of a mass-and energy-conserved finite element method for the Schrödinger …
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