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Year 2018, Volume: 1 Issue: 3, 202 - 205, 30.12.2018
https://doi.org/10.33187/jmsm.460001

Abstract

References

  • [1] M. Toda, Theory of Nonlinear Lattices, Springer-Verlag, New-York, 1989.
  • [2] K. Kajiwara,J. Satsuma, The conserved quantities and symmetries of the two-dimensional Toda lattice hierarchy, J. Math. Phys., 32 (1991), 506—514.
  • [3] J. J. Mohan, G. V. S. R. Deekshitulu, Fractional order difference equations, Int. J. Differ. Equ., 2012(2012), Article ID 780619, 11 pages, https://doi.org/10.1155/2012/780619.
  • [4] M. Cui, Compact finite difference method for the fractional diffusion equation J. Comput. Phys., 228 (2009), 7792–7804.
  • [5] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [6] C. Li, F. Zeng, Numerical Methods for Fractional Calculus CRC Press, Boca Raton, 2015.

Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation

Year 2018, Volume: 1 Issue: 3, 202 - 205, 30.12.2018
https://doi.org/10.33187/jmsm.460001

Abstract

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.

References

  • [1] M. Toda, Theory of Nonlinear Lattices, Springer-Verlag, New-York, 1989.
  • [2] K. Kajiwara,J. Satsuma, The conserved quantities and symmetries of the two-dimensional Toda lattice hierarchy, J. Math. Phys., 32 (1991), 506—514.
  • [3] J. J. Mohan, G. V. S. R. Deekshitulu, Fractional order difference equations, Int. J. Differ. Equ., 2012(2012), Article ID 780619, 11 pages, https://doi.org/10.1155/2012/780619.
  • [4] M. Cui, Compact finite difference method for the fractional diffusion equation J. Comput. Phys., 228 (2009), 7792–7804.
  • [5] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [6] C. Li, F. Zeng, Numerical Methods for Fractional Calculus CRC Press, Boca Raton, 2015.
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Refet Polat 0000-0001-9761-8787

Publication Date December 30, 2018
Submission Date September 14, 2018
Acceptance Date November 13, 2018
Published in Issue Year 2018 Volume: 1 Issue: 3

Cite

APA Polat, R. (2018). Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation. Journal of Mathematical Sciences and Modelling, 1(3), 202-205. https://doi.org/10.33187/jmsm.460001
AMA Polat R. Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation. Journal of Mathematical Sciences and Modelling. December 2018;1(3):202-205. doi:10.33187/jmsm.460001
Chicago Polat, Refet. “Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation”. Journal of Mathematical Sciences and Modelling 1, no. 3 (December 2018): 202-5. https://doi.org/10.33187/jmsm.460001.
EndNote Polat R (December 1, 2018) Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation. Journal of Mathematical Sciences and Modelling 1 3 202–205.
IEEE R. Polat, “Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation”, Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, pp. 202–205, 2018, doi: 10.33187/jmsm.460001.
ISNAD Polat, Refet. “Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation”. Journal of Mathematical Sciences and Modelling 1/3 (December 2018), 202-205. https://doi.org/10.33187/jmsm.460001.
JAMA Polat R. Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation. Journal of Mathematical Sciences and Modelling. 2018;1:202–205.
MLA Polat, Refet. “Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation”. Journal of Mathematical Sciences and Modelling, vol. 1, no. 3, 2018, pp. 202-5, doi:10.33187/jmsm.460001.
Vancouver Polat R. Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation. Journal of Mathematical Sciences and Modelling. 2018;1(3):202-5.

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