Mathematical and numerical analysis for some nonlinear second-order ordinary differential equations of Duffing type
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908295626752000 |
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| author | Kunimoto, Yusuke Fukuda, Ikki |
| author_facet | Kunimoto, Yusuke Fukuda, Ikki |
| contents | In this paper, we consider the initial value problem for some nonlinear second-order ODEs of Duffing type. We study the large time behavior of the solutions to this problem, from both the perspectives of mathematical and numerical analysis. First, we derive the decay estimate of the solutions, by using the energy method. Moreover, we numerically investigate the large time behavior of the energy function related to this problem, by using a structure-preserving difference method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mathematical and numerical analysis for some nonlinear second-order ordinary differential equations of Duffing type Kunimoto, Yusuke Fukuda, Ikki Classical Analysis and ODEs 34D05, 65L12 In this paper, we consider the initial value problem for some nonlinear second-order ODEs of Duffing type. We study the large time behavior of the solutions to this problem, from both the perspectives of mathematical and numerical analysis. First, we derive the decay estimate of the solutions, by using the energy method. Moreover, we numerically investigate the large time behavior of the energy function related to this problem, by using a structure-preserving difference method. |
| title | Mathematical and numerical analysis for some nonlinear second-order ordinary differential equations of Duffing type |
| topic | Classical Analysis and ODEs 34D05, 65L12 |
| url | https://arxiv.org/abs/2504.00803 |