benjamin - bona - mahoney - burgers方程的局部人工边界条件

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-11 DOI:10.1016/j.aml.2025.109747

Qian Deng, Hongwei Li

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引用次数: 0

摘要

Benjamin-Bona-Mahony-Burgers方程模拟了小振幅长波，使其数值解的研究具有科学意义。然而，由于无界性和非线性，在无界域上进行数值求解具有一定的挑战性。为了解决这一问题，我们将人工边界方法与算子分裂方法相结合，构造了高阶局部人工边界条件，将原始问题简化为截断的有界域。严格分析了约简问题的稳定性。数值结果证实了所提方法的准确性，算例揭示了其中的物理原理。

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Local artificial boundary conditions for the Benjamin–Bona–Mahony–Burgers equation

The Benjamin–Bona–Mahony–Burgers equation models small-amplitude long waves, making the study of its numerical solutions scientifically significant. However, solving it numerically in unbounded domains is challenging due to the unboundedness and nonlinearity. To address this, we combine the artificial boundary method with an operator splitting approach to construct high-order local artificial boundary conditions, reducing the original problem to a truncated bounded domain. The stability of the reduced problem is rigorously analyzed. Numerical results confirm the accuracy of the proposed method, and computational examples reveal the underlying physics.

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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.