Abstract
In this paper, the numerical solution to the regularized long wave (GRLW) equation is investigated numerically applying two different techniques a Parabolic Monge Ampere (PMA) moving mesh and uniform mesh. The PMA moving mesh is a method for generating a moving mesh which moves as the solution moves with time. The generated mesh is obtained by having the gradient of a grid potential function. I use here the centred finite differences for both schemes. The comparison between these schemes is shown in the last table and figure. The analytical solution is derived in Appendix A. I find a solution when it has only one solitary wave. Next, I show when it has two or three solitary waves. Figures 2D and 3D shows all of these numerical results using the mentioned schemes compared with the exact solution.