Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation
This paper deals with the numerical solution of space-time fractional partial differential-difference Toda lattice equation $\frac{\partial^{2\alpha} u_n}{\partial x^{\alpha}\partial t^{\alpha}}=(1+\frac{\partial^\alpha u_n}{\partial t^{\alpha}})(u_{n-1}-2u_n+u_{n+1})$, $\alpha \in (0,1)$. The finit...
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| Format: | Article |
| Language: | English |
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Mahmut Akyigit
2018-12-01
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| Series: | Journal of Mathematical Sciences and Modelling |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/612950 |
| _version_ | 1797350502174818304 |
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| author | Refet Polat |
| author_facet | Refet Polat |
| author_sort | Refet Polat |
| collection | DOAJ |
| description | This paper deals with the numerical solution of space-time fractional partial differential-difference Toda lattice equation $\frac{\partial^{2\alpha} u_n}{\partial x^{\alpha}\partial t^{\alpha}}=(1+\frac{\partial^\alpha u_n}{\partial t^{\alpha}})(u_{n-1}-2u_n+u_{n+1})$, $\alpha \in (0,1)$. The finite differences method (FD-method) is used for numerical solution of this problem. According to the method, we approximate the unknown values $u_n$ of the desired function by finite differences approximation. As an application we demonstrate the capabilities of this method for identification of various values of order of fractional derivative $\alpha$. Numerical results show that the proposed version of FD-method allows to obtain all data from the initial and boundary conditions with enough high accuracy. |
| first_indexed | 2024-03-08T12:46:49Z |
| format | Article |
| id | doaj.art-db394fca9dcc4c75beb44ac13fe6c8c9 |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T12:46:49Z |
| publishDate | 2018-12-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-db394fca9dcc4c75beb44ac13fe6c8c92024-01-21T07:33:11ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922018-12-011320220510.33187/jmsm.4600011408Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice EquationRefet PolatThis paper deals with the numerical solution of space-time fractional partial differential-difference Toda lattice equation $\frac{\partial^{2\alpha} u_n}{\partial x^{\alpha}\partial t^{\alpha}}=(1+\frac{\partial^\alpha u_n}{\partial t^{\alpha}})(u_{n-1}-2u_n+u_{n+1})$, $\alpha \in (0,1)$. The finite differences method (FD-method) is used for numerical solution of this problem. According to the method, we approximate the unknown values $u_n$ of the desired function by finite differences approximation. As an application we demonstrate the capabilities of this method for identification of various values of order of fractional derivative $\alpha$. Numerical results show that the proposed version of FD-method allows to obtain all data from the initial and boundary conditions with enough high accuracy.https://dergipark.org.tr/tr/download/article-file/612950finite differences methodtoda lattice equationspace-time fractional differential-difference equationstoda lattice equation |
| spellingShingle | Refet Polat Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation Journal of Mathematical Sciences and Modelling finite differences method toda lattice equation space-time fractional differential-difference equations toda lattice equation |
| title | Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation |
| title_full | Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation |
| title_fullStr | Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation |
| title_full_unstemmed | Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation |
| title_short | Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation |
| title_sort | finite difference solution to the space time fractional partial differential difference toda lattice equation |
| topic | finite differences method toda lattice equation space-time fractional differential-difference equations toda lattice equation |
| url | https://dergipark.org.tr/tr/download/article-file/612950 |
| work_keys_str_mv | AT refetpolat finitedifferencesolutiontothespacetimefractionalpartialdifferentialdifferencetodalatticeequation |