Convergence analysis and an efficient numerical technique for the solution of Benjamin Bona Mahony partial differential equation. (10th January 2023)

• Record Type: Journal Article
• Authors: Rawat, Ashish Kumar; Deep, Gagan; Dhiman, Neeraj; Chauhan, Anand
• Is Part Of: International journal of mathematical modelling and numerical optimisation. Volume 13:Number 2(2023)
• Page Start: 105
• Page End: 122
• Publication Date: 2023-01-10
• Subjects: Benjamin Bona Mahony equation -- BBM -- MCTB-spline functions -- collocation technique -- stability analysis -- convergence analysis; Mathematical models -- Periodicals; Mathematical optimization -- Periodicals; 519.605
• Languages: English
• ISSNs: 2040-3607

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.