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Abstract and Applied Analysis
Volume 2012, Article ID 514103, 10 pages
Research Article

Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

Received 19 March 2012; Accepted 19 May 2012

Academic Editor: Ferhan M. Atici

Copyright © 2012 Reza Mokhtari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.