Novel comparison of numerical and analytical methods for fractional Burger–Fisher equation

Abstract

<p style='text-indent:20px;'>In this paper, we investigate some analytical, numerical and approximate analytical methods by considering time-fractional nonlinear Burger–Fisher equation (FBFE). (1/G<inline-formula><tex-math id="M1">\begin{document}$ ' $\end{document}</tex-math></inline-formula>)-expansion method, finite difference method (FDM) and Laplace perturbation method (LPM) are considered to solve the FBFE. Firstly, we obtain the analytical solution of the mentioned problem via (1/G<inline-formula><tex-math id="M2">\begin{document}$ ' $\end{document}</tex-math></inline-formula>)-expansion method. Also, we compare the numerical method solutions and point out which method is more effective and accurate. We study truncation error, convergence, Von Neumann's stability principle and analysis of linear stability of the FDM. Moreover, we investigate the <inline-formula><tex-math id="M3">\begin{document}$ L_{2} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ L_\infty $\end{document}</tex-math></inline-formula> 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 perturbation method. Nonetheless, both of these methods are totally settlement in obtaining efficient results of fractional order differential equations.