A comparative study for the numerical approximation of 1D and 2D hyperbolic telegraph equations with UAT and UAH tension B-spline DQM

IF 2.4 Q2 ENGINEERING, MECHANICAL
Mamta Kapoor
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引用次数: 0

Abstract

Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while the second implemented regime is uniform algebraic hyperbolic tension B-spline DQM. The resulting system of ODEs is solved by the SSP RK43 method after the aforementioned equations are spatially discretized. To assess the success of chosen tactics, a comparison of errors is shown. The graphs can be seen, and it is asserted that the precise and numerical results are in agreement with one another. Analyses of convergence and stability are also given. It should be highlighted that there is a dearth of study on 1D and 2D hyperbolic telegraph equations. This aim of this study is to efficiently create results with fewer mistakes. These techniques would surely be useful for other higher-order nonlinear complex natured partial differential equations, including fractional equations, integro equations, and partial-integro equations.
用UAT和UAH张力b样条DQM进行一维和二维双曲电报方程数值逼近的比较研究
摘要本文对比了一维和二维双曲电报方程的两种数值形式。第一种实现形式为均匀代数三角张力b样条DQM,第二种实现形式为均匀代数双曲张力b样条DQM。将上述方程进行空间离散化后,用SSP RK43方法求解得到的ode系统。为了评估所选战术的成功,给出了错误的比较。图中可以看到,并断言,精度和数值结果是一致的。并给出了收敛性和稳定性分析。应该强调的是,目前缺乏对一维和二维双曲电报方程的研究。这项研究的目的是有效地创造更少错误的结果。这些技术对于其他高阶非线性复杂性质的偏微分方程,包括分数阶方程、积分方程和部分积分方程,肯定是有用的。
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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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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