A new way of deriving implicit Runge-Kutta methods based on repeated integrals
<|reference_start|>A new way of deriving implicit Runge-Kutta methods based on repeated integrals: Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a new way of deriving coefficients of implicit Runge-Kutta methods. This approach based on repeated integrals yields both new and well-known Butcher's tableaux. We discuss the properties of newly derived methods and compare them with standard collocation implicit Runge-Kutta methods in a series of numerical experiments. In particular, we observe higher accuracy and higher experimental order of convergence of some newly derived methods.<|reference_end|>
@article{mizerová2024a,
    title={A new way of deriving implicit Runge-Kutta methods based on repeated
  integrals},
    author={Hana Mizerov'a, Katar'ina Tvrd'a},
    journal={arXiv preprint arXiv:2404.16665},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.16665},
    primaryClass={math.NA cs.NA}
}