We study the strong existence and uniqueness of solutions within a Weyl chamber for a class of particle systems driven by multiplicative noise. This class includes well-known processes in physics and mathematical finance. We propose a method to prove the existence of negative moments for the solutions. This result allows us to analyze two numerical schemes for approximating the solutions. The first scheme is a backward Euler--Maruyama scheme, which ensures that the approximated solution remains within the Weyl chamber. The second scheme is a truncated and backward Euler--Maruyama scheme, which produces values in Euclidean space instead of the Weyl chamber, offering improved computational efficiency. This talk is based on joint works with Minh-Thang Do (Institute of Mathematics, Vietnam Academy of Science and Technology) and Hoang-Long Ngo (Hanoi National University of Education).