Nonstandard Finite Difference Method for Solving Complex-Order Fractional Burgers' Equations

Abstract

The aim of this work is to present numerical treatments to a complex order fractional nonlinear one-dimensional problem of Burgers' equations. A new parameter sigma(t) is presented in order to be consistent with the physical model problem. This parameter characterizes the existence of fractional structures in the equations. A relation between the parameter sigma(t) and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finite-difference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.