应用数学和力学2026，Vol.47Issue(4)：505-515,11.DOI:10.21656/1000-0887.450288
二维Fisher-KPP方程的一组显式单调的有限差分法
A Class of Explicit and Monotonic Finite Difference Methods for 2D Fisher-KPP Equations
摘要
Abstract
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.关键词
Fisher-KPP方程/保正性/有界性/单调性/有限差分法Key words
Fisher-KPP equation/positivity preservation/boundedness/monotonicity/finite difference method分类
数理科学引用本文复制引用
张佳豪,邓定文..二维Fisher-KPP方程的一组显式单调的有限差分法[J].应用数学和力学,2026,47(4):505-515,11.基金项目
国家自然科学基金(12461070) （12461070）
江西省自然科学基金重点项目(20242BAB26005) （20242BAB26005）
江西省杰出青年基金(20212ACB211006) （20212ACB211006）
