Fully Discrete Local Discontinuous Galerkin method for the generalized Benjamin-Ono equation
<|reference_start|>Fully Discrete Local Discontinuous Galerkin method for the generalized Benjamin-Ono equation: The main purpose of this paper is to design a local discontinuous Galerkin (LDG) method for the Benjamin-Ono equation. We analyze the stability and error estimates for the semi-discrete LDG scheme. We prove that the scheme is $L^2$-stable and it converges at a rate $\mathcal{O}(h^{k+1/2})$ for general nonlinear flux. Furthermore, we develop a fully discrete LDG scheme using the four-stage fourth order Runge-Kutta method and ensure the devised scheme is strongly stable in case of linear flux using two-step and three-step stability approach under an appropriate time step constraint. Numerical examples are provided to validate the efficiency and accuracy of the method.<|reference_end|>
@article{dwivedi2024fully,
    title={Fully Discrete Local Discontinuous Galerkin method for the generalized
  Benjamin-Ono equation},
    author={Mukul Dwivedi and Tanmay Sarkar},
    journal={arXiv preprint arXiv:2405.08360},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.08360},
    primaryClass={math.NA cs.NA}
}