Mathematical analysis of a conservative numerical scheme for the Ostrovsky equation

Abstract

We consider a conservative scheme for the Ostrovsky equation proposed in Yaguchi et al. (J. Comput. Appl. Math., 2010), whose mathematical analysis has been left open. In this letter, we first show the existence of numerical solutions. We then establish an $L^2$ convergence estimate, which can in turn imply an $H^1$ estimate by a supplementary $L^\infty$ boundedness argument. We also point out that the scheme can be implemented in a differential form, which is much cheaper in computational cost.