Eventual Periodicity of Linearized BBM Equation using RBFs Meshless Method.

Abstract

Among the class of dispersive wave equations the BBM equation (Benjamin-Bona-Mahony) is a notable model for long surface gravity waves inside shallow water with small amplitude propagating unidirectionally and has been broadly utilized in research facility and in field investigation of water waves. One more specific subjective part of arrangement for a number of wave equations demonstrated by investigations, which connect along with their large-time behavior named as eventual time periodicity uncovered across solutions to IBVPs (initial-boundaryvalue-problems). In the present study eventual periodicity of solutions for the linearized BBM equation (IBVP) on a half-line coupled with periodic boundary condition will be explored numerically utilizing meshless technique dependent on RBFs.