تقرير
Low regularity error estimates for the time integration of 2D NLS
| العنوان: | Low regularity error estimates for the time integration of 2D NLS |
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| المؤلفون: | Ji, Lun, Ostermann, Alexander, Rousset, Frédéric, Schratz, Katharina |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M12, 65M15, 35Q55 |
| الوصف: | A filtered Lie splitting scheme is proposed for the time integration of the cubic nonlinear Schr\"odinger equation on the two-dimensional torus $\mathbb{T}^2$. The scheme is analyzed in a framework of discrete Bourgain spaces, which allows us to consider initial data with low regularity; more precisely initial data in $H^s(\mathbb{T}^2)$ with $s>0$. In this way, the usual stability restriction to smooth Sobolev spaces with index $s>1$ is overcome. Rates of convergence of order $\tau^{s/2}$ in $L^2(\mathbb{T}^2)$ at this regularity level are proved. Numerical examples illustrate that these convergence results are sharp. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2301.10639 |
| رقم الأكسشن: | edsarx.2301.10639 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |