Rodas6P and Tsit5DA - two new Rosenbrock-type methods for DAEs
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908677042077696 |
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| author | Steinebach, Gerd |
| author_facet | Steinebach, Gerd |
| contents | Two new Rosenbrock methods for solving index-1 differential algebraic equations are presented. Rodas6P is a sixth-order method based on the same design principles as the Rodas3P, Rodas4P, and Rodas5P methods. Tsit5DA is based on an explicit solution approach for the differential equations and a linear-implicit approach for the algebraic equations. Such a fourth-order method has already been presented in Rentrop, Roche & Steinebach, 1989. Tsit5DA now provides a significantly improved fifth-order method which is based on the well known Tsit5 method. The theoretical properties of the new methods are verified by some order tests and benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rodas6P and Tsit5DA - two new Rosenbrock-type methods for DAEs Steinebach, Gerd Numerical Analysis 65L04, 65L80, 68N15 Two new Rosenbrock methods for solving index-1 differential algebraic equations are presented. Rodas6P is a sixth-order method based on the same design principles as the Rodas3P, Rodas4P, and Rodas5P methods. Tsit5DA is based on an explicit solution approach for the differential equations and a linear-implicit approach for the algebraic equations. Such a fourth-order method has already been presented in Rentrop, Roche & Steinebach, 1989. Tsit5DA now provides a significantly improved fifth-order method which is based on the well known Tsit5 method. The theoretical properties of the new methods are verified by some order tests and benchmarks. |
| title | Rodas6P and Tsit5DA - two new Rosenbrock-type methods for DAEs |
| topic | Numerical Analysis 65L04, 65L80, 68N15 |
| url | https://arxiv.org/abs/2511.21252 |