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arXiv · 1910.13700

Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schr\"odinger equation in one and two dimensions

Ziyuan Liu·Hong Zhang·Xu Qian·Songhe Song
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Abstract

We present and analyze a series of conservative diagonally implicit Runge--Kutta schemes for the nonlinear Schr\"odiner equation. With the application of the newly developed invariant energy quadratization approach, these schemes possess not only high accuracy , high order convergence (up to fifth order) and efficiency due to diagonally implicity but also mass and energy conservative properties. Both theoretical analysis and numerical experiments of one- and two-dimensional dynamics are carried out to verify the invariant conservative properties, convergence orders and longtime simulation stability.

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Ziyuan Liu, Hong Zhang, Xu Qian, Songhe Song. 2019-10-30. Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schr\"odinger equation in one and two dimensions. https://arxiv.org/abs/1910.13700

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