A CWENO large time-step scheme for Hamilton--Jacobi equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916137975939072 |
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| author | Carlini, E. Ferretti, R. Preda, S. Semplice, M. |
| author_facet | Carlini, E. Ferretti, R. Preda, S. Semplice, M. |
| contents | We propose a high order numerical scheme for time-dependent first order Hamilton--Jacobi--Bellman equations. In particular we propose to combine a semi-Lagrangian scheme with a Central Weighted Non-Oscillatory reconstruction. We prove a convergence result in the case of state- and time-independent Hamiltonians.
Numerical simulations are presented in space dimensions one and two, also for more general state- and time-dependent Hamiltonians, demonstrating superior performance in terms of CPU time gain compared with a semi-Lagrangian scheme coupled with Weighted Non-Oscillatory reconstructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15367 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A CWENO large time-step scheme for Hamilton--Jacobi equations Carlini, E. Ferretti, R. Preda, S. Semplice, M. Numerical Analysis Optimization and Control 65N12, 65M10, 49L25 We propose a high order numerical scheme for time-dependent first order Hamilton--Jacobi--Bellman equations. In particular we propose to combine a semi-Lagrangian scheme with a Central Weighted Non-Oscillatory reconstruction. We prove a convergence result in the case of state- and time-independent Hamiltonians. Numerical simulations are presented in space dimensions one and two, also for more general state- and time-dependent Hamiltonians, demonstrating superior performance in terms of CPU time gain compared with a semi-Lagrangian scheme coupled with Weighted Non-Oscillatory reconstructions. |
| title | A CWENO large time-step scheme for Hamilton--Jacobi equations |
| topic | Numerical Analysis Optimization and Control 65N12, 65M10, 49L25 |
| url | https://arxiv.org/abs/2402.15367 |