Recent Advances in Numerical Solutions for Hamilton-Jacobi PDEs
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.
Cite
@article{arxiv.2502.20833,
title = {Recent Advances in Numerical Solutions for Hamilton-Jacobi PDEs},
author = {Tingwei Meng and Siting Liu and Samy Wu Fung and Stanley Osher},
journal= {arXiv preprint arXiv:2502.20833},
year = {2026}
}