High-order Explicit Richardson Extrapolation Method for One-dimensional Fisher-KPP Equation

In this paper, an explicit difference scheme is studied for Fisher-Kolmogorov-Petrovsky-Piscounov equation. The energy analysis method is used to prove that the solution of the difference scheme is bounded when r = \alpha \dfrac\tau h^2 \leqslant \dfrac12 . It is proved that it has a convergence order of O\left( \tau + h^2 \right) in maximum norm. Then, the extrapolation solutions with convergence orders of O\left( \tau ^2 + h^２ \right) or O\left(\tau + h^4\right) or O\left(\tau^2 + h^4\right) are obtained, by developing three Richardson extrapolation methods. Finally, a numerical example is given to confirm that the numerical results are consistent with the theoretical results.