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 : 23 | Download : 12

Publication Date : 2018-12-30

Article Type : Research Paper

Abstract :This paper deals with the numerical solution of space-time fractional partial differential-difference Toda lattice equation $\frac{\partial^{2\alpha} u_n}{\partial x^{\alpha}\partial t^{\alpha}}=insert ignore into journalissuearticles values(1+\frac{\partial^\alpha u_n}{\partial t^{\alpha}});insert ignore into journalissuearticles values(u_{n-1}-2u_n+u_{n+1});$, $\alpha \in insert ignore into journalissuearticles values(0,1);$. The finite differences method insert ignore into journalissuearticles values(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