An insight on some properties of high order nonstandard linear multistep methods
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912826713440256 |
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| author | Takács, Bálint |
| author_facet | Takács, Bálint |
| contents | In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard version of Taylor's series is constructed. The preservation of some qualitative properties (boundedness, the linear combination of the components, and a property similar to monotonicity) is also proven for all step sizes. The methods are applied to a one-dimensional equation and a system of equations, in which the numerical experiments confirm the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An insight on some properties of high order nonstandard linear multistep methods Takács, Bálint Numerical Analysis 65L06, 92D25, 92D30 In this paper, nonstandard multistep methods are considered. It is shown that under some (sufficient and necessary) conditions, these methods attain the same order as their standard counterparts - to prove this statement, a nonstandard version of Taylor's series is constructed. The preservation of some qualitative properties (boundedness, the linear combination of the components, and a property similar to monotonicity) is also proven for all step sizes. The methods are applied to a one-dimensional equation and a system of equations, in which the numerical experiments confirm the theoretical results. |
| title | An insight on some properties of high order nonstandard linear multistep methods |
| topic | Numerical Analysis 65L06, 92D25, 92D30 |
| url | https://arxiv.org/abs/2505.17606 |