二维Fisher-KPP方程的一组显式单调的有限差分法OA
A Class of Explicit and Monotonic Finite Difference Methods for 2D Fisher-KPP Equations
运用一类加权的差分公式和显式 Euler 法离散扩散项及一阶时间导数项,从而对二维 Fisher-Kolmogorov-Petrovsky-Piscounov(Fisher-KPP)方程构造一组两层、显式、单调的差分格式.经分析,证明了当网格步长和参数 α,p,θ 满足一定约束条件时,该格式能够保持原问题解的保正性、有界性和单调性等数学性质,并且获得了数值解在无穷范数下的误差估计.数值实验验证了数值结果与理论结果相吻合.
With a class of weighted difference formulas and explicit Euler methods to discretize diffusion terms and the 1st-order temporal derivative,respectively,a new type of 2-level,explicit and monotonic finite differ-ence methods is established for 2D Fisher-KPP equations.Asα,p,θand the grid step size satisfy some constrai-ning conditions,their numerical solutions can inherit the properties of the exact solutions,such as positivity preservation,boundedness and monotonicity.Furthermore,the maximum norm error estimate is obtained,rig-orously.Numerical experiments illustrate that the numerical results agree well with the theoretical findings.
张佳豪;邓定文
南昌航空大学 数学与信息科学学院,南昌 330063南昌航空大学 数学与信息科学学院,南昌 330063
数理科学
Fisher-KPP方程保正性有界性单调性有限差分法
Fisher-KPP equationpositivity preservationboundednessmonotonicityfinite difference method
《应用数学和力学》 2026 (4)
505-515,11
国家自然科学基金(12461070)江西省自然科学基金重点项目(20242BAB26005)江西省杰出青年基金(20212ACB211006)
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