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首页> 外文期刊>Journal of Computational Physics >Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrodinger equation
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Two completely explicit and unconditionally convergent Fourier pseudo-spectral methods for solving the nonlinear Schrodinger equation

机译：用于求解非线性Schrodinger方程的两个完全明确的和无条件地收敛傅立叶伪光谱方法

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This paper aims to construct and analyze two new Fourier pseudo-spectral (FPS) methods for the general nonlinear Schrodinger (NLS) equation. The two FPS methods have two merits: unconditional convergence and complete explicitness in the practical computation. Further more, by introducing a modified mass functional and a modified energy functional, the two FPS methods are proved to preserve the total mass and energy in the discrete sense. Besides the standard energy method, the key techniques used in our numerical analysis are a mathematical induction argument and a lifting technique. Without any restriction on the grid ratio and initial value, we establish the optimal error estimate of the two FPS methods for solving the general NLS equation, while previous work just is valid for the cubic NLS equation and requires small initial value for the focusing case. These two FPS methods are proved to be spectrally accurate in space and second-order accurate in time, respectively. The analysis framework can be used to prove the unconditional convergence of many other Fourier pseudo-spectral methods for solving the NLS-type equations. We investigate the effect of the nonlinear term on the progression simulation of the plane wave, the conservation of the invariants and the effect of initial data on the blow-up solution via different parameters. Numerical results are reported to show the accuracy and efficiency of the proposed methods. (C) 2019 Elsevier Inc. All rights reserved.
机译：本文旨在构建和分析用于一般非线性Schrodinger（NLS）方程的两个新的傅里叶伪光谱（FPS）方法。两个FPS方法有两个优点：无条件收敛性和实际计算中的完全明确性。此外，通过引入改进的质量功能和改进的能量功能，证明了两个FPS方法以保持离散意义上的总质量和能量。除了标准能量法之外，我们数值分析中使用的关键技术是数学诱导参数和提升技术。没有对网格比和初始值的任何限制，我们建立了解决通用NLS方程的两个FPS方法的最佳误差估计，而先前的工作只是对立方NLS方程有效，并且需要对焦案例的小初始值。证明这两个FPS方法分别以空间和二阶准确地进行光谱准确。分析框架可用于证明许多其他傅立叶伪光谱方法的无条件收敛，用于求解NLS型方程。我们调查非线性术语对平面波的展进模拟的影响，通过不同参数保护不变性的避孕和初始数据的效果。据报道，数值结果显示了所提出的方法的准确性和效率。 （c）2019 Elsevier Inc.保留所有权利。

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