A Class of Explicit and Monotonic Finite Difference Methods for 2D Fisher-KPP Equations

ZHANG Jiahao; DENG Dingwen

doi:10.21656/1000-0887.450288

Volume 47 Issue 4

Apr. 2026

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ZHANG Jiahao, DENG Dingwen. A Class of Explicit and Monotonic Finite Difference Methods for 2D Fisher-KPP Equations[J]. Applied Mathematics and Mechanics, 2026, 47(4): 505-515. doi: 10.21656/1000-0887.450288

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A Class of Explicit and Monotonic Finite Difference Methods for 2D Fisher-KPP Equations

doi: 10.21656/1000-0887.450288

ZHANG Jiahao,
DENG Dingwen^,

College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, P.R.China

Received Date: 2024-10-28
Rev Recd Date: 2025-02-26
Publish Date: 2026-04-01

Abstract

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 difference methods is established for 2D Fisher-KPP equations. As α, p, θ and the grid step size satisfy some constraining 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, rigorously. Numerical experiments illustrate that the numerical results agree well with the theoretical findings.
- Fisher-KPP equation,
- positivity preservation,
- boundedness,
- monotonicity,
- finite difference method

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References

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