- Journal of Mathematical Sciences and Modelling
- Vol: 1 Issue: 3
- Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice...
Finite Difference Solution to the Space-Time Fractional Partial Differential-Difference Toda Lattice Equation
Authors : Refet Polat
Pages : 202-205
Doi:10.33187/jmsm.460001
View : 8 | Download : 5
Publication Date : 2018-12-30
Article Type : Research
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