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In this article, we are interested in the strong well-posedness together withthe numerical approximation of some one-dimensional stochastic differentialequations with a non-linear drift, in the sense of McKean-Vlasov, driven by aspectrally-positive L{\'e}vy process and a Brownian motion. We provide criteriafor the existence of strong solutions under non-Lipschitz conditions ofYamada-Watanabe type without non-degeneracy assumption. The strong convergencerate of the propagation of chaos for the associated particle system and of thecorresponding Euler-Maruyama scheme are also investigated. In particular, thestrong convergence rate of the Euler-Maruyama scheme exhibits an interplaybetween the regularity of the coefficients and the order of singularity of theL{\'e}vy measure around zero.

Well-posedness and approximation of some one-dimensional L\'evy-driven non-linear SDEs