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

Year 2018, , 202 - 205, 30.12.2018

Refet Polat

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

Cited By: 2

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.

Keywords

Finite differences method, Toda lattice equation, Space-time fractional differential-difference equations, Toda lattice equation

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