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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| Format: | Article |
| Language: | English |
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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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| author | Reza Mokhtari Fereshteh Toutian Isfahani Maryam Mohammadi |
| author_facet | Reza Mokhtari Fereshteh Toutian Isfahani Maryam Mohammadi |
| author_sort | Reza Mokhtari |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2b6ed4f3400347dab18e9d8ef5ba3895 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2b6ed4f3400347dab18e9d8ef5ba38952025-02-03T06:00:05ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/514103514103Reproducing Kernel Method for Solving Nonlinear Differential-Difference EquationsReza Mokhtari0Fereshteh Toutian Isfahani1Maryam Mohammadi2Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, IranDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, IranDepartment of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, IranOn 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.http://dx.doi.org/10.1155/2012/514103 |
| spellingShingle | Reza Mokhtari Fereshteh Toutian Isfahani Maryam Mohammadi Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations Abstract and Applied Analysis |
| title | Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations |
| title_full | Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations |
| title_fullStr | Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations |
| title_full_unstemmed | Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations |
| title_short | Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations |
| title_sort | reproducing kernel method for solving nonlinear differential difference equations |
| url | http://dx.doi.org/10.1155/2012/514103 |
| work_keys_str_mv | AT rezamokhtari reproducingkernelmethodforsolvingnonlineardifferentialdifferenceequations AT fereshtehtoutianisfahani reproducingkernelmethodforsolvingnonlineardifferentialdifferenceequations AT maryammohammadi reproducingkernelmethodforsolvingnonlineardifferentialdifferenceequations |