Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929522468716544 |
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| author | Ando', Alessia Vermiglio, Rossana |
| author_facet | Ando', Alessia Vermiglio, Rossana |
| contents | Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be recast as abstract differential equations, which motivates the present work. The result is a general approach that allows us to define the methods explicitly and analyze their convergence properties in a unifying way. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_00498 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework Ando', Alessia Vermiglio, Rossana Numerical Analysis 65L03, 65L04, 65L06, 65R20, 34K05, 45D05, 47D03 Exponential Runge-Kutta methods for semilinear ordinary differential equations can be extended to abstract differential equations, defined on Banach spaces. Thanks to the sun-star theory, both delay differential equations and renewal equations can be recast as abstract differential equations, which motivates the present work. The result is a general approach that allows us to define the methods explicitly and analyze their convergence properties in a unifying way. |
| title | Exponential Runge-Kutta methods for delay equations in the sun-star abstract framework |
| topic | Numerical Analysis 65L03, 65L04, 65L06, 65R20, 34K05, 45D05, 47D03 |
| url | https://arxiv.org/abs/2410.00498 |