A new approach to modified regularized long wave equation

In this paper, a homotopy analysis method employed to obtain approximate numerical solution of the modified regularized long wave (MRLW) equation with some specified initial conditions. The results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme. The proposed technique solves the nonlinear problems without using Adomian polynomials and He's polynomials, which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation method. Numerical results are presented graphically, and tabular form reveals that the homotopy analysis method is an effective and convenient method to solve MRLW equation.