Numerical approximations of CNLS equations via UAH tension B-spline DQM

IF 2.4 Q2 ENGINEERING, MECHANICAL Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0283
Mamta Kapoor, V. Joshi
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Abstract

Abstract Via UAH tension B-spline DQM in the present research, numerical approximation of coupled Schrödinger equations in one and two dimensions is fetched. In the present research, a novel regime is generated as a fusion of a UAH tension B-spline of fourth-order and DQM to fetch the requisite weighting coefficients. To ensure the adaptability and effectiveness of the proposed regime, different numerical examples are elaborated. Present results are matched with previous results, and the elastic property is also validated for solitons. The fetched ordinary differential equations system is handled via the SSP-RK43 regime. The stability of the present method is verified via the matrix method. The robustness of the proposed regime is affirmed via error norms. The fetched results are acceptable and validated. Elasticity property via wave interaction is also covered in the present research. The present study also focuses on one very important property of physics, like elasticity, which is rarely discussed in the literature. The developed numerical regime will undoubtedly be useful in addressing various fractional partial differential equations of complex nature as well.
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基于UAH张力b样条DQM的CNLS方程数值逼近
摘要本研究通过UAH张力b样条DQM,得到了一维和二维耦合Schrödinger方程的数值逼近。在本研究中,将四阶UAH张力b样条与DQM融合生成一个新的区域,以获得所需的加权系数。为了保证所提机制的适应性和有效性,给出了不同的数值算例。本文的结果与以往的结果相吻合,并验证了孤子的弹性性质。所得到的常微分方程组通过SSP-RK43域进行处理。通过矩阵法验证了该方法的稳定性。该方法的鲁棒性通过误差范数得到了验证。获取的结果是可接受的,并且经过验证。本文还研究了波浪相互作用下的弹性特性。目前的研究还集中在一个非常重要的物理性质,如弹性,这在文献中很少讨论。所发展的数值体系无疑也将有助于解决各种复杂性质的分数阶偏微分方程。
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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