2024/09/29 by Francesca R. Crucinio, Crucinio, Francesca R., Adam M. Johansen +1
Engineering · Mathematics · #45B05 #65C35 #65K10 #65Rxx #Advanced Mathematical Physics Problems #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Methodology (stat.ME) #Nanofluid Flow and Heat Transfer #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2409.19642
openalex publication_date 2024/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by a recent method for approximate solution of Fredholm equations of the first kind, we develop a corresponding method for a class of Fredholm equations of the second kind. In particular, we consider the class of equations for which the solution is a probability measure. The approach centres around specifying a functional whose gradient flow admits a minimizer corresponding to a regularized version of the solution of the underlying equation and using a mean-field particle system to approximately simulate that flow. Theoretical support for the method is presented, along with some illustrative numerical results.