ABSTRACT
This paper presents a finite element scheme for numerical solutions of the Gilson-Pickering (G-P) equation by using septic B-spline functions as approximate functions. Firstly we study optimal-order L²-error estimates for standard Galerkin semi-discrete approximation using smooth splines on a uniform mesh for periodic initial value problem of the G-P equation. A Von-Neumann stability analysis of the algorithm has been performed as well. Moreover, reliableness and practicalness of the presented method is demonstrated by analyzing behavior
of single soliton. The L2 and L∞ error norms and two lowest invariants I1 and I2 of the equa-tion have been computed to control proficiency and conservation properties of the suggested algorithm. Obtained numerical results have been illustrated with tables and graphics for easy visualization of properties of the problem modelled. Also the results indicate that our method is favorable.