Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations

Reza Mokhtari, Fereshteh Toutian Isfahani and Maryam Mohammadi

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

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 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.

Date: 2012
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https://doi.org/10.1155/2012/514103

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:514103

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