NOVEL COMPARISON OF NUMERICAL AND ANALYTICAL METHODS FOR FRACTIONAL BURGER-FISHER EQUATION - Yokus, Asif; Yavuz, Mehmet (Amer Inst Mathematical Sciences-Aims, 2021)
In this paper, we investigate some analytical, numerical and ap-proximate analytical methods by considering time-fractional nonlinear Burger- Fisher equation (FBFE). (1/G')-expansion method, finite difference method (FDM) and Laplace perturbation method (LPM) are considered to solve the FBFE. Firstly, we obtain the analytical solution of the mentioned problem via (1/G')-expansion method. Also, we compare the numerical method solutions and point out which method is more effective and accurate. We study trun-cation error, convergence, Von Neumann's stability principle and analysis of linear stability of the FDM. Moreover, we investigate the L-2 and Loo norm errors for the FDM. According to the results of this study, it can be concluded that the finite difference method has a lower error level than the Laplace per-turbation method. Nonetheless, both of these methods are totally settlement in obtaining efficient results of fractional order differential equations.
Keywords: finite difference method; Laplace perturbation method; linear stability; analytical solution; Caputo fractional derivative; Nonlinear time-fractional Burger-Fisher equation