Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations

作者：Reza Mokhtari, Fereshteh Toutian Isfahani, Maryam Mohammadi · 发表于：Abstract and Applied Analysis · 年份：2012 · DOI：10.1155/2012/514103 · 被引用次数：17 · 研究领域：Fractional Differential Equations Solutions、Differential Equations and Numerical Methods、Numerical methods in engineering

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.