Explicit radial basis function Runge-Kutta methods
<|reference_start|>Explicit radial basis function Runge-Kutta methods: The aim of this paper is to design the explicit radial basis function (RBF) Runge-Kutta methods for the initial value problem. We construct the two-, three- and four-stage RBF Runge-Kutta methods based on the Gaussian RBF Euler method with the shape parameter, where the analysis of the local truncation error shows that the s-stage RBF Runge-Kutta method could formally achieve order s+1. The proof for the convergence of those RBF Runge-Kutta methods follows. We then plot the stability region of each RBF Runge-Kutta method proposed and compare with the one of the correspondent Runge-Kutta method. Numerical experiments are provided to exhibit the improved behavior of the RBF Runge-Kutta methods over the standard ones.<|reference_end|>
@article{gu2024explicit,
    title={Explicit radial basis function Runge-Kutta methods},
    author={Jiaxi Gu, Xinjuan Chen, Jae-Hun Jung},
    journal={arXiv preprint arXiv:2403.08253},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.08253},
    primaryClass={math.NA cs.NA}
}