Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows

Francesca R. Crucinio; Adam M. Johansen

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arXiv · 2409.19642

Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows

Francesca R. Crucinio·Adam M. Johansen

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Abstract

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 \emph{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.

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BibTeX RIS

Francesca R. Crucinio, Adam M. Johansen. 2024-09-29. Solving Fredholm Integral Equations of the Second Kind via Wasserstein Gradient Flows. https://arxiv.org/abs/2409.19642

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