By using the stochastic particle method, the truncated Euler-Maruyama (TEM) method is proposed for numerically solving McKean-Vlasov stochastic differential equations (MV-SDEs), possibly with both drift and diffusion coefficients having super-linear growth in the state variable. Firstly, the result of the propagation of chaos in the L^q (q\geq 2) sense is obtained under general assumptions. Then, the standard 1/2-order strong convergence rate in the L^q sense of the proposed method corresponding to the particle system is derived by utilizing the stopping time analysis technique. Furthermore, long-time dynamical properties of MV-SDEs, including the moment boundedness, stability, and the existence and uniqueness of the invariant probability measure, can be numerically realized by the TEM method. Additionally, it is proven that the numerical invariant measure converges to the underlying one of MV-SDEs in the L^2-Wasserstein metric. Finally, the conclusions obtained in this paper are verified through examples and numerical simulations.

翻译：通过采用随机粒子方法，针对状态变量中漂移系数和扩散系数可能具有超线性增长的McKean-Vlasov随机微分方程（MV-SDEs），提出了截断欧拉-丸山（TEM）方法进行数值求解。首先，在一般性假设下获得了L^q（q≥2）意义下的混沌传播结果。随后，利用停时分析技术，推导出所提方法对应粒子系统在L^q意义下具有标准1/2阶强收敛速率。此外，TEM方法可数值实现MV-SDEs的长期动力学特性，包括矩有界性、稳定性以及不变概率测度的存在唯一性。进一步证明，数值不变测度在L^2-Wasserstein度量下收敛于MV-SDEs的原始不变测度。最后，通过算例与数值仿真验证了本文所得结论。