Numerical solutions of ordinary differential equations using Spline-Integral Operator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914960745955328 |
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| author | Salgado, Gustavo H. O. Romanelli, João P. R. |
| author_facet | Salgado, Gustavo H. O. Romanelli, João P. R. |
| contents | In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical solutions of ordinary differential equations using Spline-Integral Operator Salgado, Gustavo H. O. Romanelli, João P. R. Numerical Analysis 65L05, 65L07 In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order. |
| title | Numerical solutions of ordinary differential equations using Spline-Integral Operator |
| topic | Numerical Analysis 65L05, 65L07 |
| url | https://arxiv.org/abs/2409.20369 |