半经典极限下离焦Davey-Stewartson II方程的渐近保持格式

IF 2.3 2区 数学 Q1 MATHEMATICS, APPLIED
Dandan Wang, Hanquan Wang
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引用次数: 0

摘要

本文致力于构造离焦Davey-Stewartson II方程在半经典极限下的渐近保持方法。首先,对方程引入Wentzel-Kramers-Brillouin ansatz $\varPsi =A^\varepsilon e^{i\phi ^\varepsilon /\varepsilon }$,得到了$A^\varepsilon $和$\phi ^\varepsilon $的新系统,其中复值振幅函数$A^\varepsilon $可以自动避免真空中量子势的奇异性。其次,对$t\in [0,T]$证明了新系统解的局部存在性,并证明了新系统解在$\varepsilon \rightarrow 0$时收敛于极限。最后,我们为新系统构造了二阶分时傅里叶谱方法,大量的数值实验表明,该方法对于$\varepsilon $是一致精确的,即它的精度不会因$\varepsilon $消失而下降,并且是渐近保持的。然而,它可能不是一致收敛的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An asymptotic preserving scheme for the defocusing Davey–Stewartson II equation in the semiclassical limit
This article is devoted to constructing an asymptotic preserving method for the defocusing Davey–Stewartson II equation in the semiclassical limit. First, we introduce the Wentzel–Kramers–Brillouin ansatz $\varPsi =A^\varepsilon e^{i\phi ^\varepsilon /\varepsilon }$ for the equation and obtain the new system for both $A^\varepsilon $ and $\phi ^\varepsilon $, where the complex-valued amplitude function $A^\varepsilon $ can avoid automatically the singularity of the quantum potential in vacuum. Secondly, we prove the local existence of the solutions of the new system for $t\in [0,T]$, and show that the solutions of the new system are convergent to the limit when $\varepsilon \rightarrow 0$. Finally, we construct a second-order time-splitting Fourier spectral method for the new system and numerous numerical experiments show that the method is uniformly accurate with respect to $\varepsilon $, i.e., its accuracy does not deteriorate for vanishing $\varepsilon $, and it is an asymptotic preserving one. However, it might not be uniformly convergent.
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来源期刊
IMA Journal of Numerical Analysis
IMA Journal of Numerical Analysis 数学-应用数学
CiteScore
5.30
自引率
4.80%
发文量
79
审稿时长
6-12 weeks
期刊介绍: The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects. Occasional survey articles are also published.
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