Convergence and stability of randomized implicit two-stage Runge-Kutta schemes
<|reference_start|>Convergence and stability of randomized implicit two-stage Runge-Kutta schemes: We randomize the implicit two-stage Runge-Kutta scheme in order to improve the rate of convergence (with respect to a deterministic scheme) and stability of the approximate solution (with respect to the solution generated by the explicit scheme). For stability analysis, we use Dahlquist's concept of A-stability, adopted to randomized schemes by considering three notions of stability: asymptotic, mean-square, and in probability. The randomized implicit RK2 scheme proves to be A-stable asymptotically and in probability but not in the mean-square sense.<|reference_end|>
@article{bochacik2024convergence,
    title={Convergence and stability of randomized implicit two-stage Runge-Kutta
  schemes},
    author={Tomasz Bochacik, Pawe{l} Przyby{l}owicz, {L}ukasz Stk{e}pie'n},
    journal={arXiv preprint arXiv:2404.19059},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.19059},
    primaryClass={math.NA cs.NA}
}