Non–Polynomial Quintic Spline Method for solving the generalized regularized long wave (GRLW) equation

Abstract In this paper, a new technique for solving the generalized regularized long wave (GRLW) equation is investigated. This technique depends on a combination of the non–polynomial quintic spline method (NPQSM) with the finite difference approximation and Crank–Nicolson scheme. The stability analysis of the present method is concluded using the Von–Neumann method. Also, the most popular three invariants of motion of GRLW equation are obtained for the given problems and their numerical results are compared with the analytical values. In addition, a comparison between the present method and the previous methods and the error norms L2 and L∞ are presented to show the accuracy of the suggested method.