Abstract
In the present work, the new quartic trigonometric B-spline approach based on finite difference scheme is described to solve the one dimensional non-linear equation of (Benjamin – Bona-Mahony-Burger). Dirichlet boundary with the help of applying the von-Neumann stability analysis is also used in this description. While the time derivative part is discretized by using the finite difference scheme. In the space dimension, the quartic trigonometric B-spline is also used as an interpolation function. The execution of this method which is used in the present work showed that the quartic trigonometric B-spline method is a more efficient and effective tool and gives better results according to the comparisons that are made with the precise solution for a different time and some other published numerical methods.
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