Year: 2023
Type: preprint
Abstract: We introduce a novel monotone discretization method for addressing obstacle problems involving the integral fractional Laplacian with homogeneous Dirichlet boundary conditions over bounded Lipschitz domains. This problem is prevalent in mathematical finance, particle systems, and elastic theory. By leveraging insights from the successful monotone discretization of the fractional Laplacian, we establish uniform boundedness, solution existence, and uniqueness for the numerical solutions of the fractional obstacle problem. We employ a policy iteration approach for efficient solution of discrete nonlinear problems and prove its finite convergence. Our improved policy iteration, adapted to solution regularity, demonstrates superior performance by modifying discretization across different regions. Numerical examples underscore the method's efficacy.
Source: arXiv (Cornell University)
Authors: Han, Rubing, Wu, Shuonan, Zhou, Hao
Institution: Peking University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4385245484