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 unun is constructed by truncating the series to nn terms. The convergence of unun 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.