Non-polynomial spline method for solving the generalized regularized long wave equation

Abstract

In this paper, non-polynomial spline method for solving the generalized regularized long wave (GRLW) equation are presented. In this paper, we take deferent spline functions. The stability analysis using Von-Neumann technique shows the scheme is marginally stable. To test accuracy the error normsL2, L∞ are computed. Also, the change in conservation quantities are evaluated which are found to be very small. To illustrate the applicability and efficiency of the basis, we compare obtained numerical results with other existing recent methods. Moreover, interaction two and three solitary waves are shown. The development of the Maxwellian initial condition into solitary waves is also shown and we show that the number of solitons which are generated from the Maxwellian initial condition can be determined

Keywords

• Non-polynomial spline, generalized regularized long wave equation, solitary waves, solitons