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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 L₂, L∞ and three invariants I₁,I₂ and I₃ 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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Karakoç et al. (2021) studied this question.
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