论文标题
非线性schrödinger方程
Mass- and energy-preserving exponential Runge-Kutta methods for the nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，通过将标量辅助变量方法与指数runge-kutta方法相结合，为非线性schrödinger方程开发了一个任意高阶结构传播的指数runge-kutta方法。通过引入辅助变量，我们首先将原始模型转换为等效系统，该系统同时既可以接受质量和修改的节能定律。然后在时间上应用Lawson方法和Symbletic Runge-Kutta方法，我们得出了一类质量和能量能量的时间 - 二散方案，这些方案是任意高阶的时间。对数值实验进行了解决，以证明新提出的方案的准确性和有效性。
In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schrödinger equation by combining the scalar auxiliary variable approach with the exponential Runge-Kutta method. By introducing an auxiliary variable, we first transform the original model into an equivalent system which admits both mass and modified energy conservation laws. Then applying the Lawson method and the symplectic Runge-Kutta method in time, we derive a class of mass- and energy-preserving time-discrete schemes which are arbitrarily high-order in time. Numerical experiments are addressed to demonstrate the accuracy and effectiveness of the newly proposed schemes.
