On General Linearly Implicit Quantized State System Methods
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909971205062656 |
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| author | Bergonzi, Mariana Fernández, Joaquín Kofman, Ernesto |
| author_facet | Bergonzi, Mariana Fernández, Joaquín Kofman, Ernesto |
| contents | This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using this idea, two novel sub-families of algorithms are designed that improve the performance of current LIQSS methods while preserving their properties regarding stability, global error bound and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classic numerical integration algorithms is also analyzed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On General Linearly Implicit Quantized State System Methods Bergonzi, Mariana Fernández, Joaquín Kofman, Ernesto Numerical Analysis Performance This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using this idea, two novel sub-families of algorithms are designed that improve the performance of current LIQSS methods while preserving their properties regarding stability, global error bound and efficient event handling capabilities. The features of the new algorithms are studied in two application examples where the advantages over classic numerical integration algorithms is also analyzed. |
| title | On General Linearly Implicit Quantized State System Methods |
| topic | Numerical Analysis Performance |
| url | https://arxiv.org/abs/2512.17855 |