具有立方非线性的薛定谔方程的线性化欧拉 Galerkin 方案的新误差分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED Applied Mathematics Letters Pub Date : 2024-11-25 DOI:10.1016/j.aml.2024.109401

Huaijun Yang

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引用次数: 0

摘要

本文研究了线性化欧拉 Galerkin 方案，并在无任何时间步长限制的情况下，为具有立方非线性的薛定谔方程获得了 L2 规范下的无条件最优误差估计。分析的关键在于通过数学归纳法对两种情况下的数值解与精确解的里兹投影之间的 H1 规范进行约束，而不是之前工作中使用的误差分割技术。最后，我们给出了一些数值结果来证实理论分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A new error analysis of a linearized Euler Galerkin scheme for Schrödinger equation with cubic nonlinearity

In this paper, a linearized Euler Galerkin scheme is studied and the unconditionally optimal error estimate in

L^{2}

-norm is obtained for Schrödinger equation with cubic nonlinearity without any time-step restriction. The key to the analysis is to bound the

H^{1}

-norm between the numerical solution and the Ritz projection of the exact solution by mathematical induction for two cases rather than the error splitting technique used in the previous work. Finally, some numerical results are presented to confirm the theoretical analysis.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.