Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations
<|reference_start|>Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations: We study the spatially homogeneous granular medium equation \[\partial_t\mu=\rm{div}(\mu\nabla V)+\rm{div}(\mu(\nabla W \ast \mu))+\Delta\mu\,,\] within a large and natural class of the confinement potentials $V$ and interaction potentials $W$. The considered problem do not need to assume that $\nabla V$ or $\nabla W$ are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.<|reference_end|>
@article{benko2024convergence,
    title={Convergence rates of particle approximation of forward-backward
  splitting algorithm for granular medium equations},
    author={Matej Benko, Iwona Chlebicka, J{o}rgen Endal, B{l}a.zej Miasojedow},
    journal={arXiv preprint arXiv:2405.18034},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.18034},
    primaryClass={math.NA cs.NA stat.CO}
}