New probabilistic methods for physics

TL;DR

This paper introduces probabilistic models to analyze the long-term behavior of iterative methods, with applications to ordinary differential equations and mechanics problems in multidimensional spaces.

Contribution

It proposes novel probabilistic approaches to understand asymptotic behaviors in iterative algorithms and mechanics, expanding the analytical toolkit for these fields.

Findings

Probabilistic models effectively describe iteration asymptotics.

Applications demonstrate utility in ODE and mechanics problems.

Provides new insights into iterative process behaviors.

Abstract

We present how a probabilistic model can describe the asymptotic behavior of the iterations, with applications for ODE and approach of some problems in mechanics in $\mathbb{R}^d$.