An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher-Kolmogorov-Petrovsky-Piskunov Equation

Sangkwon Kim; Chaeyoung Lee; Hyun Geun Lee; Hyundong Kim; Soobin Kwak; Youngjin Hwang; Seungyoon Kang; Seokjun Ham; Junseok Kim

doi:10.1155/2021/7300471

An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher-Kolmogorov-Petrovsky-Piskunov Equation

Sangkwon Kim, Chaeyoung Lee, Hyun Geun Lee, Hyundong Kim, Soobin Kwak, Youngjin Hwang, Seungyoon Kang, Seokjun Ham, Junseok Kim

Department of Mathematics

Korea University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this study, we present an unconditionally stable positivity-preserving numerical method for the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation in the one-dimensional space. The Fisher-KPP equation is a reaction-diffusion system that can be used to model population growth and wave propagation. The proposed method is based on the operator splitting method and an interpolation method. We perform several characteristic numerical experiments. The computational results demonstrate the unconditional stability, boundedness, and positivity-preserving properties of the proposed scheme.

Original language	English
Article number	7300471
Journal	Discrete Dynamics in Nature and Society
Volume	2021
DOIs	https://doi.org/10.1155/2021/7300471
State	Published - 2021

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title = "An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher-Kolmogorov-Petrovsky-Piskunov Equation",

abstract = "In this study, we present an unconditionally stable positivity-preserving numerical method for the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation in the one-dimensional space. The Fisher-KPP equation is a reaction-diffusion system that can be used to model population growth and wave propagation. The proposed method is based on the operator splitting method and an interpolation method. We perform several characteristic numerical experiments. The computational results demonstrate the unconditional stability, boundedness, and positivity-preserving properties of the proposed scheme.",

author = "Sangkwon Kim and Chaeyoung Lee and Lee, {Hyun Geun} and Hyundong Kim and Soobin Kwak and Youngjin Hwang and Seungyoon Kang and Seokjun Ham and Junseok Kim",

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T1 - An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher-Kolmogorov-Petrovsky-Piskunov Equation

AU - Kim, Sangkwon

AU - Lee, Chaeyoung

AU - Lee, Hyun Geun

AU - Kim, Hyundong

AU - Kwak, Soobin

AU - Hwang, Youngjin

AU - Kang, Seungyoon

AU - Ham, Seokjun

AU - Kim, Junseok

PY - 2021

Y1 - 2021

N2 - In this study, we present an unconditionally stable positivity-preserving numerical method for the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation in the one-dimensional space. The Fisher-KPP equation is a reaction-diffusion system that can be used to model population growth and wave propagation. The proposed method is based on the operator splitting method and an interpolation method. We perform several characteristic numerical experiments. The computational results demonstrate the unconditional stability, boundedness, and positivity-preserving properties of the proposed scheme.

AB - In this study, we present an unconditionally stable positivity-preserving numerical method for the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation in the one-dimensional space. The Fisher-KPP equation is a reaction-diffusion system that can be used to model population growth and wave propagation. The proposed method is based on the operator splitting method and an interpolation method. We perform several characteristic numerical experiments. The computational results demonstrate the unconditional stability, boundedness, and positivity-preserving properties of the proposed scheme.

UR - http://www.scopus.com/inward/record.url?scp=85118546993&partnerID=8YFLogxK

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DO - 10.1155/2021/7300471

M3 - Article

AN - SCOPUS:85118546993

SN - 1026-0226

VL - 2021

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

M1 - 7300471

ER -

An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher-Kolmogorov-Petrovsky-Piskunov Equation

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