Energy-superconvergent Runge-Kutta Time Discretizations
<|reference_start|>Energy-superconvergent Runge-Kutta Time Discretizations: In this paper, we investigate the energy accuracy of explicit Runge-Kutta (RK) time discretization for antisymmetric autonomous linear systems and present a framework for constructing RK methods with an order of energy accuracy much greater than the number of stages. For an $s$-stage, $p$th-order RK method, we show that the energy accuracy can achieve superconvergence with an order up to $2s-p+1$ if $p$ is even. Several energy-superconvergent methods, including five- to seven-stage fourth-order methods with energy accuracy up to the eleventh order, together with their strong stability criteria, are derived. The proposed methods are examined using several applications, including second-order ordinary differential equations for harmonic oscillators, linear integro-differential equations for peridynamics, and one-dimensional Maxwell's equations of electrodynamics.<|reference_end|>
@article{liu2024energy-superconvergent,
    title={Energy-superconvergent Runge-Kutta Time Discretizations},
    author={Jinjie Liu and Moysey Brio},
    journal={arXiv preprint arXiv:2405.05448},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.05448},
    primaryClass={math.NA cs.NA}
}