Theory and internal structure of ADER-DG method for ordinary differential equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918444570509312 |
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| author | Popov, I. S. |
| author_facet | Popov, I. S. |
| contents | Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$- and $AN$-stable, $L$-stable, $B$- and $BN$-stable, and algebraically stable. Several other relations useful for an application and implementation of the ADER-DG method are proved. Applications of the ADER-DG method demonstrated compliance with the expected theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13824 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theory and internal structure of ADER-DG method for ordinary differential equations Popov, I. S. Numerical Analysis Spectral Theory Applied Physics Computational Physics 65L05, 65L60, 65L20, 65L06 Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$- and $AN$-stable, $L$-stable, $B$- and $BN$-stable, and algebraically stable. Several other relations useful for an application and implementation of the ADER-DG method are proved. Applications of the ADER-DG method demonstrated compliance with the expected theoretical results. |
| title | Theory and internal structure of ADER-DG method for ordinary differential equations |
| topic | Numerical Analysis Spectral Theory Applied Physics Computational Physics 65L05, 65L60, 65L20, 65L06 |
| url | https://arxiv.org/abs/2508.13824 |