Reproducing kernel method for solving nonlinear differential-difference equations (Q448719)

Summary: 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.