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

The generalized time‐fractional Fisher's equation is a substantial model for illustrating the system's dynamics. Studying effective numerical methods for this equation has considerable scientific importance and application value. In that direction, this paper presents designing and analyzing a high‐order numerical scheme for the generalized time‐fractional Fisher's equation. The time‐fractional derivative is taken in the Caputo sense and approximated using Euler backward discretization. The quasilinearization technique is used to linearize the problem, and then a compact finite difference scheme is considered for discretizing the equation in space direction. Our numerical method is convergent of Ok2−α+h4$$ O\left({k}^{2-\alpha }+{h}^4\right) $$, where h$$ h $$ and k$$ k $$ are step sizes in spatial and temporal directions, respectively. Three problems are tested numerically by implementing the proposed technique, and the acquired results reveal that the proposed method is suitable for solving this problem. [ABSTRACT FROM AUTHOR]