More Accurate Solutions for Approximate Solutions of the Benjamin Bona Mahony Equation with A New Technique

Abstract

In the field of mathematical modeling, numerical calculations for natural systems and obtaining travelling wave solutions of nonlinear wave equations in relation to sciences like optics, fluid mechanics, solid state physics, plasma physics, kinetics, and geology have recently gained significant importance. Numerous approaches have been proposed for this. The method used in this article is to get more accurate numerical solutions for the Benjamin Bona Mahony (BBM) equation, one of the equations used to simulate the aforementioned nonlinear phenomena. This is accomplished by applying the Lie-Trotter splitting technique to the BBM equation. First, the problem is divided into two subproblems with derivatives with respect to time, one of which is linear and the other of which is nonlinear. Secondly, the galerkin finite element method (FEM) based on the cubic B-spline approximate functions for spatial discretization and the practical classical finite difference approaches for temporal discretization is used to reduce each subproblem to the algebraic equation system. The Lie Trotter splitting algorithm is then used to solve the obtained systems. Explanatory test problems are taken into consideration, demonstrating the newly suggested algorithm's superior accuracy over earlier approaches. Tables and graphs display the numerical results generated by the suggested algorithm. The new approach's stability analysis is also looked at. In light of the outcomes and the price of Matlab computation software, it is appropriate to say that this new method can be applied with ease to partial differential equations used in other fields.

Keywords

• Cubic B-splines
• Galerkin method
• BBM equation
• Lie Trotter splitting

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