Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations
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 tr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/514103 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |