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

Refet POLAT

doi:https://doi.org/10.33187/jmsm.460001

Article Details

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

Authors:

Refet POLAT

Publisher:

Mahmut AKYİĞİT

Main Topics:

Mathematics

Journal:

Journal of Mathematical Sciences and Modelling 2018 Vol.1 Issue 3, pp.202-205

Document Type:

Article

Publication Date:

12/2018

Document Language:

English

Document ID (Org No.):

2000486709

Frequency:

Monthly

pISSN:

2636-8692

DOI:

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 ∂2αun∂xα∂tα=(1+∂αun∂tα)(un−1−2un+un+1)∂2αun∂xα∂tα=(1+∂αun∂tα)(un−1−2un+un+1)\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}), α∈(0,1)α∈(0,1)\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 ununu_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 αα\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.

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Article Details

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

Authors: Refet POLAT

Publisher: Mahmut AKYİĞİT

Main Topics: Mathematics

Journal: Journal of Mathematical Sciences and Modelling 2018 Vol.1 Issue 3, pp.202-205

Document Type: Article

Publication Date: 12/2018

Document Language: English

Document ID (Org No.): 2000486709

Frequency: Monthly

pISSN: 2636-8692

DOI: https://doi.org/10.33187/jmsm.460001

Issues

Authors:

Refet POLAT

Publisher:

Mahmut AKYİĞİT

Main Topics:

Mathematics

Journal:

Journal of Mathematical Sciences and Modelling 2018 Vol.1 Issue 3, pp.202-205

Document Type:

Article

Publication Date:

12/2018

Document Language:

English

Document ID (Org No.):

2000486709

Frequency:

Monthly

pISSN:

2636-8692

DOI:

https://doi.org/10.33187/jmsm.460001