Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition
The numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic eq...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/434976 |
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| _version_ | 1832556526917648384 |
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| author | Allaberen Ashyralyev Fadime Dal |
| author_facet | Allaberen Ashyralyev Fadime Dal |
| author_sort | Allaberen Ashyralyev |
| collection | DOAJ |
| description | The numerical and analytic solutions of the mixed
problem for multidimensional fractional hyperbolic partial
differential equations with the Neumann condition are presented. The
stable difference scheme for the numerical solution of the mixed
problem for the multidimensional fractional hyperbolic equation with
the Neumann condition is presented. Stability estimates for the
solution of this difference scheme and for the first- and second-order difference derivatives are obtained. A procedure of modified
Gauss elimination method is used for solving this difference scheme
in the case of one-dimensional fractional hyperbolic partial
differential equations. He's variational iteration method is
applied. The comparison of these methods is presented. |
| format | Article |
| id | doaj-art-e053ea3219554799bf3135ab6fae4fa7 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e053ea3219554799bf3135ab6fae4fa72025-02-03T05:45:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/434976434976Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann ConditionAllaberen Ashyralyev0Fadime Dal1Department of Mathematics, Fatih University, Buyukcekmece 34500, Istanbul, TurkeyDepartment of Mathematics, Ege University, 35100 Izmir, TurkeyThe numerical and analytic solutions of the mixed problem for multidimensional fractional hyperbolic partial differential equations with the Neumann condition are presented. The stable difference scheme for the numerical solution of the mixed problem for the multidimensional fractional hyperbolic equation with the Neumann condition is presented. Stability estimates for the solution of this difference scheme and for the first- and second-order difference derivatives are obtained. A procedure of modified Gauss elimination method is used for solving this difference scheme in the case of one-dimensional fractional hyperbolic partial differential equations. He's variational iteration method is applied. The comparison of these methods is presented.http://dx.doi.org/10.1155/2012/434976 |
| spellingShingle | Allaberen Ashyralyev Fadime Dal Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition Discrete Dynamics in Nature and Society |
| title | Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition |
| title_full | Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition |
| title_fullStr | Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition |
| title_full_unstemmed | Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition |
| title_short | Finite Difference and Iteration Methods for Fractional Hyperbolic Partial Differential Equations with the Neumann Condition |
| title_sort | finite difference and iteration methods for fractional hyperbolic partial differential equations with the neumann condition |
| url | http://dx.doi.org/10.1155/2012/434976 |
| work_keys_str_mv | AT allaberenashyralyev finitedifferenceanditerationmethodsforfractionalhyperbolicpartialdifferentialequationswiththeneumanncondition AT fadimedal finitedifferenceanditerationmethodsforfractionalhyperbolicpartialdifferentialequationswiththeneumanncondition |