Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Numerical Analysis
2025-11-18 v2 Numerical Analysis
Pattern Formation and Solitons
Abstract
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods using implicit-explicit (additive) Runge-Kutta methods that are implicit in the stiff linear part. The new discretization of the hyperbolization conserves important invariants converging to invariants of the BBM equation. We use the entropy relaxation approach to make the fully discrete schemes energy-preserving. Numerical experiments demonstrate the effectiveness of these discretizations.
Keywords
Cite
@article{arxiv.2511.10044,
title = {Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation},
author = {Sebastian Bleecke and Abhijit Biswas and David I. Ketcheson and Hendrik Ranocha and Jochen Schutz},
journal= {arXiv preprint arXiv:2511.10044},
year = {2025}
}