Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations

Reza Mokhtari, Fereshteh Toutian Isfahani and Maryam Mohammadi

Abstract and Applied Analysis, 2012, vol. 2012, 1-10

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 ð ‘¢ ð ‘› , ð ‘š is constructed by truncating the series to ð ‘š terms. The convergence of ð ‘¢ ð ‘› , ð ‘š 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:514103

DOI: 10.1155/2012/514103

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