正则对数Schrödinger方程的能量守恒rk - fem

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2024-12-19 DOI:10.1016/j.camwa.2024.12.009

Changhui Yao, Lei Li, Huijun Fan, Yanmin Zhao

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引用次数: 0

摘要

针对具有周期边界条件的正则对数Schrödinger方程（RLogSE），构造了一种具有能量守恒的高阶隐显有限元方法。离散格式包括时间方向上的松弛外推龙格-库塔（RERK）法和空间方向上的有限元法。选择合适的松弛参数是实现能量守恒的关键技术。利用时空分割技术，在不受时间步长τ和网格尺寸h限制的情况下，给出了l2范数和h1范数的最优误差估计。数值算例验证了理论结果。

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Energy-preserving RERK-FEM for the regularized logarithmic Schrödinger equation

A high-order implicit–explicit (IMEX) finite element method with energy conservation is constructed to solve the regularized logarithmic Schrödinger equation (RLogSE) with a periodic boundary condition. The discrete scheme consists of the relaxation-extrapolated Runge–Kutta (RERK) method in the temporal direction and the finite element method in the spatial direction. Choosing a proper relaxation parameter for the RERK method is the key technique for energy conservation. The optimal error estimates in the L2-norm and H1-norm are provided without any restrictions between time step size τ and mesh size h by temporal–spatial splitting technology. Numerical examples are given to demonstrate the theoretical results.

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来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).