一维Fisher-KPP方程的高阶显式Richardson外推法  

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

作　　者：赵紫琳 邓定文[1] ZHAO Zi-lin;DENG Ding-wen(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2022年第1期17-22,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(11861047);江西省自然科学基金(20202BABL201005);江西省杰出青年基金(20212ACB211006)。

摘　　要：通过研究一维Fisher-Kolmogorov-Petrovsky-Piscounov(Fisher-KPP)方程的显式差分格式,并运用能量分析法证明了当r=αr/h^(2)≤1/2时差分格式的解是有界的,且在无穷范数意义下有O(τ+h^(2))的收敛阶。然后发展了三种外Richardson推法,分别得到收敛阶为O(τ^(2)+h^(2)),O(τ+h^(4))和O(τ^(2)+h^(4))的外推解。数值实验表明,数值结果与理论结果是吻合的。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=αr/h^(2)≤1/2.It is proved that it has a convergence order of O(τ+h^(2))in maximum norm.Then,the extrapolation solutions with convergence orders of O(τ^(2)+h^(2))or O(τ+h~4)or O(τ~2+h^(4))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.

关 键 词：Fisher-KPP方程 显式差分格式 有界性 RICHARDSON外推法 

分 类 号：O214.82[理学—概率论与数理统计]