Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Abstract EN

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 un,m is constructed by truncating the series to m terms.

The convergence of un,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.