二维Fisher-KPP方程的显式Richardson外推法  

The Explicit Richardson Extrapolation Method for Two-Dimensional Fisher-KPP Equation

作　　者：李志君 

机构地区：[1]南昌航空大学,数学与信息科学学院,江西 南昌

出　　处：《理论数学》2021年第9期1649-1656,共8页Pure Mathematics

摘　　要：本文研究二维Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP)方程的显式差分格式,运用能量分析法证明了在满足r =τ/h2≤1/4时,差分格式的解是有界的,且在无穷范数意义下有O(τ+h2)的收敛阶。然后,通过发展一类Richardson外推法,在无穷范数意义下得到了收敛阶为O(τ2+h4)的外推解。最后,数值结果验证了格式的有效性和理论结果的正确性。In this paper, an explicit difference scheme is investigated for two-dimensional Fisher-KPP equation. Under the condition of r =τ/h2≤1/4, the boundedness of the solution of the difference scheme is proven using the energy analysis method. It is proved that it has a convergence order of O(τ+h2) in maximum norm. Then by developing a class of Richardson extrapolation method, the extrapola-tion solution with convergence order of O(τ2+h4) in maximum norm is obtained. Finally, numeri-cal results confirm the efficiency of the schemes and the correctness of theoretical results.

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

分 类 号：O17[理学—数学]