Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-26 DOI:10.3390/sym15111980
Akeel A. AL-saedi, Omid Nikan, Zakieh Avazzadeh, António M. Lopes
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Abstract

This paper addresses a numerical approach for computing the solitary wave solutions of the generalized Rosenau–Kawahara–RLW model established by coupling the generalized Rosenau–Kawahara and Rosenau–RLW equations. The solution of this model is accomplished by using the finite difference approach and the upwind local radial basis functions-finite difference. Firstly, the PDE is transformed into a nonlinear ODEs system by means of the radial kernels. Secondly, a high-order ODE solver is implemented for discretizing the system of nonlinear ODEs. The main advantage of this technique is its lack of need for linearization. The global collocation techniques impose a significant computational cost, which arises from calculating the dense system of algebraic equations. The proposed technique estimates differential operators on every stencil. As a result, it produces sparse differentiation matrices and reduces the computational burden. Numerical experiments indicate that the method is precise and efficient for long-time simulation.
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浅水理论中具有表面张力的广义Rosenau-Kawahara-RLW方程的孤立波传播
本文讨论了由广义Rosenau-Kawahara方程和Rosenau-RLW方程耦合建立的广义Rosenau-Kawahara - rlw模型的孤立波解的数值计算方法。采用有限差分法和迎风局部径向基函数-有限差分法对该模型进行求解。首先,利用径向核将偏微分方程转化为非线性偏微分方程系统;其次,采用高阶ODE求解器对非线性ODE系统进行离散化。这种技术的主要优点是不需要线性化。全局配置技术由于需要计算密集的代数方程组,计算成本很高。该方法估计每个模板上的微分算子。因此,它产生稀疏的微分矩阵,减少了计算量。数值实验表明,该方法对长时间的模拟精度高、效率高。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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