Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential-difference equations (NDDEs) is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution u(n,m) is constructed by truncating the series to m terms. The convergence of u(n,m) 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 differential-difference problems.