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We study an implementation of the theoretical splitting scheme introduced in[Chassagneux and Yang, 2022] for singular FBSDEs [Carmona and Delarue 2013] andtheir associated quasi-linear degenerate PDEs. The fully implementablealgorithm is based on particles approximation of the transport operator andtree like approximation of the diffusion operator appearing in the theoreticalsplitting. We prove the convergence with a rate of our numerical method undersome reasonable conditions on the coefficients functions. This validates aposteriori some numerical results obtained in [Chassagneux and Yang, 2022]. Weconclude the paper with a numerical section presenting various implementationsof the algorithm and discussing their efficiency in practice.

Convergence of particles and tree based scheme for singular FBSDEs