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Nonstandard finite difference method for solving complex-order fractional Burgers’ equations

The aim of this work is to present numerical treatments to a complex order fractional nonlinear onedimensional problem of Burgers’ equations. A new parameter rt 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 rt and the time derivative complex order is derived. An unconditionally stable numerical scheme using a kind of weighted average nonstandard finitedifference discretization is presented. Stability analysis of this method is studied. Numerical simulations are given to confirm the reliability of the proposed method. |