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

Abstract

We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du−du_xx+u_x ◦dW+u^pu_xdt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.