On modified Euler methods for McKean–Vlasov stochastic differential equations with super-linear coefficients

We introduce a new class of numerical methods for solving McKean–Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the drift and diffusion coefficients. Under certain non-globally Lipschitz conditions, the proposed numerical approaches have half-order convergence in the strong sense to the corresponding system of interacting particles associated with McKean–Vlasov SDEs. By leveraging a result on the propagation of chaos, we establish the full convergence rate of the modified Euler approximations to the solution of the McKean–Vlasov SDEs. Numerical experiments are included to validate the theoretical results.