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arXiv · 2502.20833

Recent Advances in Numerical Solutions for Hamilton-Jacobi PDEs

Tingwei Meng·Siting Liu·Samy Wu Fung·Stanley Osher
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Abstract

Hamilton-Jacobi partial differential equations (HJ PDEs) play a central role in many applications such as economics, physics, and engineering. These equations describe the evolution of a value function which encodes valuable information about the system, such as action, cost, or level sets of a dynamic process. Their importance lies in their ability to model diverse phenomena, ranging from the propagation of fronts in computational physics to optimal decision-making in control systems. This paper provides a review of some recent advances in numerical methods to address challenges such as high-dimensionality, nonlinearity, and computational efficiency. By examining these developments, this paper sheds light on important techniques and emerging directions in the numerical solution of HJ PDEs.

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Tingwei Meng, Siting Liu, Samy Wu Fung, Stanley Osher. 2025-12-30. Recent Advances in Numerical Solutions for Hamilton-Jacobi PDEs. https://arxiv.org/abs/2502.20833

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