Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Abstract

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.