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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.03728 |
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Table of Contents:
- A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a high order correction to the Lax-Friedrich's method while utilizing a novel cutoff to preserve the convergence properties of the Lax-Friedrich's approximation. Since monotone methods are limited to first order accuracy by the Godunov barrier, the proposed approach provides a template for boosting the accuracy of a monotone method using a modified numerical moment stabilizer with a high-order auxiliary boundary condition. Numerical tests are provided to test the utility of the approach while a novel admissibility and stability analysis technique lays a foundation for analyzing non-monotone methods.