二维Fisher-KPP方程的显式Richardson外推法
The Explicit Richardson Extrapolation Method for Two-Dimensional Fisher-KPP Equation
DOI: 10.12677/PM.2021.119183, PDF,    国家自然科学基金支持
作者: 李志君：南昌航空大学，数学与信息科学学院，江西 南昌
关键词: Fisher-KPP方程；显式差分格式；收敛性；Richardson外推法；Fisher-KPP Equation； Explicit Difference Scheme； Convergence； Richardson Extrapolation Method
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。
Abstract: 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.
文章引用：李志君. 二维Fisher-KPP方程的显式Richardson外推法[J]. 理论数学, 2021, 11(9): 1649-1656. https://doi.org/10.12677/PM.2021.119183

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