Strong Langmuir turbulence dynamics through the trigonometric quintic and exponential B-spline schemes

Mostafa M. A. Khater; A. El-Sayed Ahmed; Mostafa M. A. Khater; A. El-Sayed Ahmed

doi:10.3934/math.2021349

AIMS Mathematics

2021, Volume 6, Issue 6: 5896-5908. doi: 10.3934/math.2021349

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Strong Langmuir turbulence dynamics through the trigonometric quintic and exponential B-spline schemes

Mostafa M. A. Khater ^{1,2
,
,},
A. El-Sayed Ahmed ³

1.
Department of Mathematics, Faculty of Science, Jiangsu University, 212013, Zhenjiang, China
2.
Department of Mathematics, Obour High Institute For Engineering and Technology, 11828, Cairo, Egypt
3.
Department of Mathematics, Faculty of Science, Taif University P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 31 December 2020 Accepted: 17 March 2021 Published: 26 March 2021
MSC : 35C07, 76B25, 81Q05, 49M05

In this manuscript, two recent numerical schemes (the trigonometric quintic and exponential cubic B-spline schemes) are employed for evaluating the approximate solutions of the nonlinear Klein-Gordon-Zakharov model. This model describes the interaction between the Langmuir wave and the ion-acoustic wave in a high-frequency plasma. The initial and boundary conditions are constructed via a novel general computational scheme. ^[1] has used five different numerical schemes, such as the Adomian decomposition method, Elkalla-expansion method, three-member of the well-known cubic B-spline schemes. Consequently, the comparison between our solutions and that have been given in ^[1], shows the accuracy of seven recent numerical schemes along with the considered model. The obtained numerical solutions are sketched in two dimensional and column distribution to explain the matching between the computational and numerical simulation. The novelty, originality, and accuracy of this research paper are explained by comparing the obtained numerical solutions with the previously obtained solutions.
Citation: Mostafa M. A. Khater, A. El-Sayed Ahmed. Strong Langmuir turbulence dynamics through the trigonometric quintic and exponential B-spline schemes[J]. AIMS Mathematics, 2021, 6(6): 5896-5908. doi: 10.3934/math.2021349

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Abstract

In this manuscript, two recent numerical schemes (the trigonometric quintic and exponential cubic B-spline schemes) are employed for evaluating the approximate solutions of the nonlinear Klein-Gordon-Zakharov model. This model describes the interaction between the Langmuir wave and the ion-acoustic wave in a high-frequency plasma. The initial and boundary conditions are constructed via a novel general computational scheme. ^[1] has used five different numerical schemes, such as the Adomian decomposition method, Elkalla-expansion method, three-member of the well-known cubic B-spline schemes. Consequently, the comparison between our solutions and that have been given in ^[1], shows the accuracy of seven recent numerical schemes along with the considered model. The obtained numerical solutions are sketched in two dimensional and column distribution to explain the matching between the computational and numerical simulation. The novelty, originality, and accuracy of this research paper are explained by comparing the obtained numerical solutions with the previously obtained solutions.

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