Funding: This work was supported by the National Natural Science Foundation of China (Grant Nos. 12226313 and 12226319), Shandong Provincial Natural Science Foundation (Grant Nos. ZR2023ZD33 and ZR2019BA002).

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ABSTRACT

In this article, we delve into the efficient artificial boundary method, specifically focusing on its application in solving the coupled sine-Gordon equations on unbounded domains, which are widely used in a variety of scientific fields. By incorporating the operator splitting approach, we have designed local artificial boundary conditions that effectively address the challenges posed by the unbounded nature of the physical domain and the intricate nonlinearities involved. These conditions are specifically developed for the coupled sine-Gordon equations, ensuring that wave outgoing boundaries are achieved without any reflections. An initial boundary value problem on a bounded computational domain is obtained, and the finite difference method is adopted to discretize the reduced problem. Rigorous analysis of the stability and convergence of the reduced problem is conducted through the introduction of an energy function. Some numerical examples are presented to demonstrate the accuracy and effectiveness of the method.

Conflicts of Interest

The authors declare no conflicts of interest.

Open Research

Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

The codes are available from the corresponding author on reasonable request.

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Volume41, Issue4

July 2025

e70015

Numerical Method and Analysis for the Coupled Sine-Gordon Equations on Unbounded Domains

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

References

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Numerical Method and Analysis for the Coupled Sine-Gordon Equations on Unbounded Domains

ABSTRACT

Conflicts of Interest

Open Research

Data Availability Statement

References

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