An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation
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...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5527728 |
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| author | Soobin Kwak Seungyoon Kang Seokjun Ham Youngjin Hwang Gyeonggyu Lee Junseok Kim |
| author_facet | Soobin Kwak Seungyoon Kang Seokjun Ham Youngjin Hwang Gyeonggyu Lee Junseok Kim |
| author_sort | Soobin Kwak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-44517015a1094abca252b1a68c78e479 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-44517015a1094abca252b1a68c78e4792025-08-20T02:17:37ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/5527728An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov EquationSoobin Kwak0Seungyoon Kang1Seokjun Ham2Youngjin Hwang3Gyeonggyu Lee4Junseok Kim5Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn 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.http://dx.doi.org/10.1155/2023/5527728 |
| spellingShingle | Soobin Kwak Seungyoon Kang Seokjun Ham Youngjin Hwang Gyeonggyu Lee Junseok Kim An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation Journal of Mathematics |
| title | An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation |
| title_full | An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation |
| title_fullStr | An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation |
| title_full_unstemmed | An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation |
| title_short | An Unconditionally Stable Difference Scheme for the Two-Dimensional Modified Fisher–Kolmogorov–Petrovsky–Piscounov Equation |
| title_sort | unconditionally stable difference scheme for the two dimensional modified fisher kolmogorov petrovsky piscounov equation |
| url | http://dx.doi.org/10.1155/2023/5527728 |
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