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June 2021 Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equation
Seydi Battal Gazi Karakoc, Khalid Karam Ali
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Tbilisi Math. J. 14(2): 33-50 (June 2021). DOI: 10.32513/tmj/19322008120

Abstract

This paper aims to obtain exact and numerical solutions of the nonlinear Benjamin Bona Mahony-Burgers (BBM-Burgers) equation. Here, we propose the modified Kudryashov method for getting the exact traveling wave solutions of BBM-Burgers equation and a septic B-spline collocation finite element method for numerical investigations. The numerical method is validated by studying solitary wave motion. Linear stability analysis of the numerical scheme is done with Fourier method based on von-Neumann theory. To show suitability and robustness of the new numerical algorithm, error norms $L_{2}$, $L_{\infty }$ and three invariants $I_{1},I_{2}$ and $I_{3}$ are calculated and obtained results are given both numerically and graphically. The obtained results state that our exact and numerical schemes ensure evident and they are penetrative mathematical instruments for solving nonlinear evolution equation.

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Seydi Battal Gazi Karakoc. Khalid Karam Ali. "Theoretical and computational structures on solitary wave solutions of Benjamin Bona Mahony-Burgers equation." Tbilisi Math. J. 14 (2) 33 - 50, June 2021. https://doi.org/10.32513/tmj/19322008120

Information

Received: 19 June 2020; Accepted: 10 November 2020; Published: June 2021
First available in Project Euclid: 2 July 2021

Digital Object Identifier: 10.32513/tmj/19322008120

Subjects:
Primary: 65N30
Secondary: 74S05, 76B25

Rights: Copyright © 2021 Tbilisi Centre for Mathematical Sciences

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Vol.14 • No. 2 • June 2021
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