تقرير
A symmetric low-regularity integrator for the nonlinear Schr\'odinger equation
| العنوان: | A symmetric low-regularity integrator for the nonlinear Schr\'odinger equation |
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| المؤلفون: | Bronsard, Yvonne Alama |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Mathematics - Analysis of PDEs |
| الوصف: | We introduce and analyze a symmetric low-regularity scheme for the nonlinear Schr\"odinger (NLS) equation beyond classical Fourier-based techniques. We show fractional convergence of the scheme in $L^2$-norm, from first up to second order, both on the torus $\mathbb{T}^d$ and on a smooth bounded domain $\Omega \subset \mathbb{R}^d$, $d\le 3$, equipped with homogeneous Dirichlet boundary condition. The new scheme allows for a symmetric approximation to the NLS equation in a more general setting than classical splitting, exponential integrators, and low-regularity schemes (i.e. under lower regularity assumptions, on more general domains, and with fractional rates). We motivate and illustrate our findings through numerical experiments, where we witness better structure preserving properties and an improved error-constant in low-regularity regimes. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2301.13109 |
| رقم الأكسشن: | edsarx.2301.13109 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |