A class of explicit implicit alternating difference schemes for generalized time fractional Fisher equation

Abstract

<abstract><p>The generalized time fractional Fisher equation is one of the significant models to describe the dynamics of the system. The study of effective numerical techniques for the equation has important scientific significance and application value. Based on the alternating technique, this article combines the classical explicit difference scheme and the implicit difference scheme to construct a class of explicit implicit alternating difference schemes for the generalized time fractional Fisher equation. The unconditional stability and convergence with order $ O\left({\tau }^{2-\alpha }+{h}^{2}\right) $ of the proposed schemes are analyzed. Numerical examples are performed to verify the theoretical analysis. Compared with the classical implicit difference scheme, the calculation cost of the explicit implicit alternating difference schemes is reduced by almost $ 60 $%. Numerical experiments show that the explicit implicit alternating difference schemes are also suitable for solving the time fractional Fisher equation with initial weak singularity and have an accuracy of order $ O\left({\tau }^{\alpha }+{h}^{2}\right) $, which verify that the methods proposed in this paper are efficient for solving the generalized time fractional Fisher equation.</p></abstract>

A high‐order numerical technique for generalized time‐fractional Fisher's equation

“…They observed the accuracy of $$$ O\left({\tau}^{2-\alpha }+{h}^2\right) $$$. Qin et al [26] proposed their study based on explicit and implicit difference schemes. They compared their results with the classical implicit difference scheme and showed that calculation cost reduces by 60 % using the proposed technique.…”