An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method

In this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The ef...

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Published inAIMS mathematics Vol. 9; no. 4; pp. 8661 - 8688
Main Authors Alrzqi, Shumoua F., Alrawajeh, Fatimah A., Hassan, Hany N.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
fast fourier transform
finite difference
fourier spectral method
gr–kdv–rlw equation
solitary waves
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Abstract In this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The efficiency, accuracy, and simplicity of the employed methodology were tested by solving eight different cases involving four examples of the single solitary wave with different parameter values, interactions between two solitary waves, interactions between three solitary waves, and evolution of solitons with Gaussian and undular bore initial conditions. The error norms were evaluated for the motion of the single solitary wave. The conservation properties of the GR–KDV–RLW equation were studied by computing the momentum and energy. Additionally, the numerical results were compared with the previous studies in the literature.
AbstractList In this article, the generalized Rosenau-Korteweg-de Vries-regularized long wave (GR–KDV–RLW) equation was numerically studied by employing the Fourier spectral collection method to discretize the space variable, while the central finite difference method was utilized for the time dependency. The efficiency, accuracy, and simplicity of the employed methodology were tested by solving eight different cases involving four examples of the single solitary wave with different parameter values, interactions between two solitary waves, interactions between three solitary waves, and evolution of solitons with Gaussian and undular bore initial conditions. The error norms were evaluated for the motion of the single solitary wave. The conservation properties of the GR–KDV–RLW equation were studied by computing the momentum and energy. Additionally, the numerical results were compared with the previous studies in the literature.
Author Alrawajeh, Fatimah A.
Hassan, Hany N.
Alrzqi, Shumoua F.
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SubjectTerms fast fourier transform
finite difference
fourier spectral method
gr–kdv–rlw equation
solitary waves
Title An efficient numerical technique for investigating the generalized Rosenau–KDV–RLW equation by using the Fourier spectral method
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