Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion (Communications in Computational Physics, 2019)
We consider a midpoint scheme to approximate analytical solutions to awhite noise driven BBM equation that readsdu−duxx+ux ◦dW+upuxdt=0.We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.