具有三次非线性的Schrödinger方程线性化BDF2 Galerkin格式的新误差分析

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-03-31 DOI:10.1016/j.camwa.2025.03.025

Huaijun Yang

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引用次数: 0

摘要

针对具有三次非线性的Schrödinger方程，提出并研究了一种线性化的2步后向微分公式（BDF2） Galerkin方法，并在不受时间步长限制的情况下获得了l2范数的无条件最优误差估计。分析的关键是用数学归纳法将数值解和精确解的里兹投影之间的h1范数绑定在两种情况下，而不是在以前的工作中使用的误差分割技术。最后给出了一些数值结果来验证理论分析。

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A new error analysis of a linearized BDF2 Galerkin scheme for Schrödinger equation with cubic nonlinearity

In this paper, a linearized 2-step backward differentiation formula (BDF2) Galerkin method is proposed and investigated for Schrödinger equation with cubic nonlinearity and unconditionally optimal error estimate in

L^{2}

-norm is obtained 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

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).