An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher-Kolmogorov-Petrovsky-Piscounov Equation

Soobin Kwak, Seungyoon Kang, Seokjun Ham, Youngjin Hwang, Gyeonggyu Lee, Junseok Kim

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we develop an unconditionally stable numerical scheme for the modified Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation modeling population dynamics in two-dimensional space. The Fisher-KPP equation models the process of interaction between reaction and diffusion. The new solution algorithm is based on an alternating direction implicit (ADI) method and an interpolation method so that it is unconditionally stable. The proposed finite difference method is second-order accurate in time and space variables. Therefore, the main purpose of this study is to propose the novel Fisher-KPP equation with a nonlinear growth term and develop an unconditionally stable second-order numerical scheme. The novelty of our method is that it is a numerical method with second-order accuracy using interpolation and ADI methods in two dimensions. We demonstrate the performance of the proposed scheme through computational tests such as convergence and stability tests and the effects of model parameters and initial conditions.

Original languageEnglish
Article number5527728
JournalJournal of Mathematics
Volume2023
DOIs
Publication statusPublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 Soobin Kwak et al.

ASJC Scopus subject areas

  • General Mathematics

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