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The mBBM equation: a mathematical key to unlocking wave behavior in fluids Cover

The mBBM equation: a mathematical key to unlocking wave behavior in fluids

International Journal of Mathematics and Computer in Engineering
Volume 3 (2025): Issue 2 (December 2025)
By: Raghda Attia Mahmoud Attia and  Mostafa Mohamed Abdelazeem Khater  
Open Access
|Sep 2024

Figures & Tables

Fig. 1

Analytical solitary wave solutions of the mBBM equation represented through diverse graphical techniques via 3D, 2D and contour plots for equations (11), (13), (15).
Analytical solitary wave solutions of the mBBM equation represented through diverse graphical techniques via 3D, 2D and contour plots for equations (11), (13), (15).

Fig. 2

Quantitative validation of analytical solutions against numerical solutions through absolute error analysis. (a–c) Absolute error between solutions obtained via the EAE method and the ECBS numerical method at defined intervals. (d–f) Absolute error comparison between solutions derived from the IKud method and ECBS numerical solutions at specified intervals.
Quantitative validation of analytical solutions against numerical solutions through absolute error analysis. (a–c) Absolute error between solutions obtained via the EAE method and the ECBS numerical method at defined intervals. (d–f) Absolute error comparison between solutions derived from the IKud method and ECBS numerical solutions at specified intervals.

Fig. 3

Comparative assessment of solution accuracy for the IKud and EAE analytical techniques, benchmarked against ECBS numerical solutions.
Comparative assessment of solution accuracy for the IKud and EAE analytical techniques, benchmarked against ECBS numerical solutions.

Fig. 4

Stream plot illustrating the propagation of solitary wave solutions in the mBBM model.
Stream plot illustrating the propagation of solitary wave solutions in the mBBM model.

Fig. 5

Comparative stream plots demonstrating the influence of parameter modifications on the propagation behavior of solitary waves in the mBBM model.
Comparative stream plots demonstrating the influence of parameter modifications on the propagation behavior of solitary waves in the mBBM model.

Quantitative assessment of solution accuracy_

Value of ℨAnalytical solutionNumerical solutionAbsolute Error
0000
0.0019.99999666666800E-049.99979867286439E-041.97993803609242E-08
0.0021.99999733333760E-031.99995893459001E-033.83987475887151E-08
0.0032.99999100003240E-032.99993640193329E-035.45980991108024E-08
0.0043.99997866680320E-033.99991146934972E-036.71974534757411E-08
0.0054.99995833375000E-034.99988333688908E-037.49968609116067E-08
0.0065.99992800103679E-035.99985120462290E-037.67964138817870E-08
0.0076.99988566890756E-036.99981427264991E-037.13962576490146E-08
0.0087.99982933770229E-037.99977174110146E-035.75966008307255E-08
0.0098.99975700787294E-038.99972281014699E-033.41977259531168E-08
0.019.99966667999946E-039.99966667999946E-030
DOI: https://doi.org/10.2478/ijmce-2025-0014 | Journal eISSN: 2956-7068
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Language: English
Page range: 171 - 184
Submitted on: Oct 11, 2023
Accepted on: Mar 31, 2024
Published on: Sep 20, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Nonlinear mBBM equation,
wave propagation,
analytical solutions,
numerical validation
Related subjects:
Computer sciences,
Computer sciences, other,
Engineering,
Introductions and overviews,
Engineering, other,
Mathematics,
General mathematics,
Physics,
Physics, other

© 2024 Raghda Attia Mahmoud Attia, Mostafa Mohamed Abdelazeem Khater, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

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