A second-order generalized BDF method for the two-dimensional (modified) Fisher-Kolmogorov-Petrovsky-Piskunov equation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911289080545280 |
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| author | Ge, Lei Zhao, Yong-Liang Shu, Qian-Yu |
| author_facet | Ge, Lei Zhao, Yong-Liang Shu, Qian-Yu |
| contents | The Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is a classical reaction-diffusion equation with broad applications such as biology, chemistry and physics. In this paper, an alternative second-order scheme is proposed by employing a shifted BDF2 method to approximate the two-dimensional (modified) Fisher-KPP equation. We both consider an uniform and a nonuniform time steps of such the scheme. The stability of the uniform discretization scheme is proved. Numerical experiments demonstrate that our uniform and non-uniform schemes are robust and accurate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14939 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A second-order generalized BDF method for the two-dimensional (modified) Fisher-Kolmogorov-Petrovsky-Piskunov equation Ge, Lei Zhao, Yong-Liang Shu, Qian-Yu Numerical Analysis The Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation is a classical reaction-diffusion equation with broad applications such as biology, chemistry and physics. In this paper, an alternative second-order scheme is proposed by employing a shifted BDF2 method to approximate the two-dimensional (modified) Fisher-KPP equation. We both consider an uniform and a nonuniform time steps of such the scheme. The stability of the uniform discretization scheme is proved. Numerical experiments demonstrate that our uniform and non-uniform schemes are robust and accurate. |
| title | A second-order generalized BDF method for the two-dimensional (modified) Fisher-Kolmogorov-Petrovsky-Piskunov equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.14939 |