A numerical method for solving the generalized tangent vector of hyperbolic systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912232829353984 |
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| author | Herty, Michael Zhou, Yizhou |
| author_facet | Herty, Michael Zhou, Yizhou |
| contents | This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challenge is addressed by developing a numerical method to compute the evolution of the generalized tangent vector introduced by Bressan and Marson (1995). Our basic strategy is to combine the conservative numerical schemes and a novel expression of the interface conditions for the tangent vectors along the discontinuity. Based on this, we propose a simple numerical method to compute the tangent vectors for general hyperbolic systems. Numerical results are presented for Burgers' equation and a 2 x 2 hyperbolic system with two genuinely nonlinear fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_04251 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A numerical method for solving the generalized tangent vector of hyperbolic systems Herty, Michael Zhou, Yizhou Numerical Analysis Optimization and Control This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challenge is addressed by developing a numerical method to compute the evolution of the generalized tangent vector introduced by Bressan and Marson (1995). Our basic strategy is to combine the conservative numerical schemes and a novel expression of the interface conditions for the tangent vectors along the discontinuity. Based on this, we propose a simple numerical method to compute the tangent vectors for general hyperbolic systems. Numerical results are presented for Burgers' equation and a 2 x 2 hyperbolic system with two genuinely nonlinear fields. |
| title | A numerical method for solving the generalized tangent vector of hyperbolic systems |
| topic | Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2412.04251 |