论文标题
通过波算子和收敛分析的2D非线性schrödinger方程的线性隐含能量的整合因子方法
Linearly implicit energy-preserving integrating factor methods for the 2D nonlinear Schrödinger equation with wave operator and convergence analysis
论文作者
论文摘要
在本文中，我们开发了一类新型的线性能量能量性能集成因子方法，用于将标量辅助变量方法和集成因子方法结合在一起，将2D非线性schrödinger方程与波动式schrödinger方程（NLSW）相结合。首先提出了二阶方案，严格证明这是能源提供的。通过使用能量方法，我们分析了其在$ H^1 $规范中的最佳收敛性，而无需对网格比率进行任何限制，在这种情况下，提出了一种新技术和改进的诱导论点来克服因数值解决方案的先验$ l^\ infty $估计而无法获得的难度。基于集成因子runge-kutta方法，我们将提出的方案扩展到任意高阶，这也是线性和保守的。提出了数值实验以确认理论分析并证明了所提出方法的优势。
In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schrödinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating factor methods. A second-order scheme is first proposed, which is rigorously proved to be energy-preserving. By using the energy methods, we analyze its optimal convergence in the $H^1$ norm without any restrictions on the grid ratio, where a novel technique and an improved induction argument are proposed to overcome the difficulty posed by the unavailability of a priori $L^\infty$ estimates of numerical solutions. Based on the integrating factor Runge-Kutta methods, we extend the proposed scheme to arbitrarily high order, which is also linear and conservative. Numerical experiments are presented to confirm the theoretical analysis and demonstrate the advantages of the proposed methods.
