New Preprint ‘Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation’ on arXiv

Sebastian Bleecke, Abhijit Biswas, Jochen Schütz, David I. Ketcheson and I have published our new preprint Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation on arXiv.

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.

The reproducibility repository is available on GitHub.