On numerical soliton and convergence analysis of Benjamin-Bona-Mahony-Burger equation via octic B-spline collocation

Abstract

In this work, we employ an octic B-spline function to construct a collocation technique for obtaining solutions to soliton on Benjamin-Bona-Mahony-Burgers (BBMB) equation. The BBMB equation is fully-discretized in two forums such as: spatial and time discretization using octic B-spline function of the unknown variable and the Crank-Nicolson procedure, respectively. The robustness of the proposed method is determined by examining four test problems. On Neumann (Fourier) method is employed to obtain unconditional stability. A convergence analysis for the current scheme is also performed, resulting in $O(h^9+(\Delta {t)}^2).$ The accuracy and efficiency of the proposed method are justified with error norms, invariants and the current result is also compared with existing results and found to be better as well as a better agreement to analytical solution. The proposed scheme is found to be more computationally efficient with $(2N+16)$ operations for whole process.

Keywords:

• BBM-Burger equation
• collocation
• convergence
• finite difference
• stability

Acknowledgements

The authors would like to thank the anonymous referees, Managing Editor and Editor in Chief for their valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.