Solving the generalized regularized long wave equation on the basis of a reproducing kernel space

On the basis of a reproducing kernel space, an iterative algorithm for solving the generalized regularized long wave equation is presented. The analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u n is constructed by truncating the series to n terms. The convergence of u n to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations.