Title: Convergence analysis and an efficient numerical technique for the solution of Benjamin Bona Mahony partial differential equation

Authors: Ashish Kumar Rawat; Gagan Deep; Neeraj Dhiman; Anand Chauhan

Addresses: Department of Mathematics, Graphic Era (Deemed to be University), Dehradun 248002, India ' Department of Computer Science and Engineering, Graphic Era (Deemed to be University), Dehradun 248002, India ' Department of Mathematics, Graphic Era Hill University, Dehradun 248002, India ' Department of Mathematics, Graphic Era (Deemed to be University), Dehradun 248002, India

Abstract: This study proposed a collocation based modified scheme of trigonometric cubic b-spline approach (MCTB-spline) to approximate the solution of the Benjamin Bona Mahony (BBM) partial differential equation. The MCTB-spline collocation method is used to discretise the space derivatives terms of the partial differential equation, while the finite difference method (FDM) is used to make discretised the time-variant derivatives of the BBM partial differential equation. This study also describes the convergency of the present method, which helps to illustrate the accuracy of the present scheme for the partial differential equation. A Rubin Graves linearisation process linearises BBM partially differential equations into nonlinear terms. An example has been selected for demonstration of numerical approximations and provided a comparative study with the previous scheme of different types of error norms. To validate the stability, Von-Neumann stability condition was applied on the proposed scheme. Results suggested that the present scheme achieved better results and outperformed the previous techniques used. We will apply the generalisation of the present scheme to higher order and coupled partial differential equations in the future.

Keywords: Benjamin Bona Mahony equation; BBM; MCTB-spline functions; collocation technique; stability analysis; convergence analysis.

DOI: 10.1504/IJMMNO.2023.129940

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.2, pp.105 - 122

Received: 11 Jun 2022
Accepted: 23 Jul 2022
Published online: 03 Apr 2023 *

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