基于非线性薛定谔方程的算子分割配位方案的数值方法

Mengli Yao, Zhifeng Weng
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引用次数: 0

摘要

本文针对非线性薛定谔方程提出了一种二阶算子分裂法与巴里心拉格朗日插值配位法相结合的方法。该方程分为线性和非线性两部分:线性部分由空间的巴里心拉格朗日插值配位法结合时间的 Crank-Nicolson 方案求解;非线性部分由于存在闭式解,可避免求解非线性代数方程,因此采用解析法求解。此外,还提供了线性子问题完全离散化方案的一致性和算子分割方案的误差估计。所提出的数值方案具有空间谱精度和时间二阶精度,大大提高了计算效率。数值实验证实了所提方法的精度、质量和能量守恒。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Numerical Method Based on Operator Splitting Collocation Scheme for Nonlinear Schrödinger Equation
In this paper, a second-order operator splitting method combined with the barycentric Lagrange interpolation collocation method is proposed for the nonlinear Schrödinger equation. The equation is split into linear and nonlinear parts: the linear part is solved by the barycentric Lagrange interpolation collocation method in space combined with the Crank–Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution, which avoids solving the nonlinear algebraic equation. Moreover, the consistency of the fully discretized scheme for the linear subproblem and error estimates of the operator splitting scheme are provided. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, mass and energy conservation of the proposed method.
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