An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation
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 prop...
Saved in:
| Main Authors: | , , , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/7300471 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556522027089920 |
|---|---|
| author | Sangkwon Kim Chaeyoung Lee Hyun Geun Lee Hyundong Kim Soobin Kwak Youngjin Hwang Seungyoon Kang Seokjun Ham Junseok Kim |
| author_facet | Sangkwon Kim Chaeyoung Lee Hyun Geun Lee Hyundong Kim Soobin Kwak Youngjin Hwang Seungyoon Kang Seokjun Ham Junseok Kim |
| author_sort | Sangkwon Kim |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a6e603037cbf4a3b94d9a8a498022e55 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a6e603037cbf4a3b94d9a8a498022e552025-02-03T05:45:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/73004717300471An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov EquationSangkwon Kim0Chaeyoung Lee1Hyun Geun Lee2Hyundong Kim3Soobin Kwak4Youngjin Hwang5Seungyoon Kang6Seokjun Ham7Junseok Kim8Department of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Kwangwoon University, Seoul 01897, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 02841, Republic of KoreaIn 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.http://dx.doi.org/10.1155/2021/7300471 |
| spellingShingle | Sangkwon Kim Chaeyoung Lee Hyun Geun Lee Hyundong Kim Soobin Kwak Youngjin Hwang Seungyoon Kang Seokjun Ham Junseok Kim An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation Discrete Dynamics in Nature and Society |
| title | An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation |
| title_full | An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation |
| title_fullStr | An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation |
| title_full_unstemmed | An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation |
| title_short | An Unconditionally Stable Positivity-Preserving Scheme for the One-Dimensional Fisher–Kolmogorov–Petrovsky–Piskunov Equation |
| title_sort | unconditionally stable positivity preserving scheme for the one dimensional fisher kolmogorov petrovsky piskunov equation |
| url | http://dx.doi.org/10.1155/2021/7300471 |
| work_keys_str_mv | AT sangkwonkim anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT chaeyounglee anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT hyungeunlee anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT hyundongkim anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT soobinkwak anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT youngjinhwang anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT seungyoonkang anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT seokjunham anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT junseokkim anunconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT sangkwonkim unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT chaeyounglee unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT hyungeunlee unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT hyundongkim unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT soobinkwak unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT youngjinhwang unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT seungyoonkang unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT seokjunham unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation AT junseokkim unconditionallystablepositivitypreservingschemefortheonedimensionalfisherkolmogorovpetrovskypiskunovequation |