Numerical approximation for non-colliding particle systems

TL;DR

This paper introduces a numerical scheme for non-colliding particle systems that preserves the non-collision property and converges strongly to the true solution, enhancing simulation accuracy for such systems.

Contribution

It applies the semi-discrete method to non-colliding particle systems, ensuring non-collision preservation and strong convergence, which is a novel adaptation of existing numerical techniques.

Findings

The scheme preserves non-collision property.

The method converges strongly to the exact solution.

Applicable to a class of non-colliding particle systems.

Abstract

We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied Mathematics, 16(1)}, to a class of non-colliding particle systems. The proposed numerical scheme preserves the non-colliding property and strongly converges to the exact solution.