Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion

Guillaume Fenger (1) , Olivier Goubet (1) , Youcef Mammeri (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du-du(xx)+u(x)circle dw+u(p)u(x)dt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.

Domaines: Mathématiques [math]

Guillaume Fenger, Olivier Goubet, Youcef Mammeri. Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion. Communications in Computational Physics, 2019, 26 (5, SI), pp.1397-1414. ⟨10.4208/cicp.2019.js60.02⟩. ⟨hal-03621774⟩