论文标题
具有多种保护和耗散定律的时间依赖性的Duhamel重新归一化方法
Time-Dependent Duhamel Renormalization method with Multiple Conservation and Dissipation Laws
论文作者
论文摘要
Cole和Musslimani引入了时间依赖的光谱重归其化（TDSR）方法，这是一种新的方法，用于解决初始边界价值问题。 TDSR方案的一个重要而新颖的方面是它以保护定律或耗散率方程式形式纳入物理学的能力。但是，该方法仅限于包含单个保守或耗散量。目前的工作大大扩展了该方法的计算特征，即（i）（i）将多个保护定律和/或耗散率方程组合，（ii）实施多功能边界条件的能力以及（iii）高阶时间整合策略。 TDSR方法应用于几个原型进化方程，具有物理意义的。示例包括Korteweg-De Vries（KDV），多维非线性Schrödinger（NLS）和Allen-Cahn方程。
The time dependent spectral renormalization (TDSR) method was introduced by Cole and Musslimani as a novel way to numerically solve initial boundary value problems. An important and novel aspect of the TDSR scheme is its ability to incorporate physics in the form of conservation laws or dissipation rate equations. However, the method was limited to include a single conserved or dissipative quantity. The present work significantly extends the computational features of the method with the (i) incorporation of multiple conservation laws and/or dissipation rate equations, (ii) ability to enforce versatile boundary conditions, and (iii) higher order time integration strategy. The TDSR method is applied on several prototypical evolution equations of physical significance. Examples include the Korteweg-de Vries (KdV), multi-dimensional nonlinear Schrödinger (NLS) and the Allen-Cahn equations.
